We show that a variety of modern deep learning tasks exhibit a 'double-descent' phenomenon where, as we increase model size, performance first gets worse and then gets better. Moreover, we show that double descent occurs not just as a function of model size, but also as a function of the number of training epochs. We unify the above phenomena by defining a new complexity measure we call the effective model complexity and conjecture a generalized double descent with respect to this measure. Furthermore, our notion of model complexity allows us to identify certain regimes where increasing (even quadrupling) the number of train samples actually hurts test performance.
The International School for Advanced Studies (SISSA) was founded in 1978 and was the first institution in Italy to promote post-graduate courses leading to a Doctor Philosophiae (or PhD) degree. A centre of excellence among Italian and international universities, the school has around 65 teachers, 100 post docs and 245 PhD students, and is located in Trieste, in a campus of more than 10 hectares with wonderful views over the Gulf of Trieste.
SISSA hosts a very high-ranking, large and multidisciplinary scientific research output. The scientific papers produced by its researchers are published in high impact factor, well-known international journals, and in many cases in the world's most prestigious scientific journals such as Nature and Science. Over 900 students have so far started their careers in the field of mathematics, physics and neuroscience research at SISSA.
ISSN: 1742-5468
Journal of Statistical Mechanics: Theory and Experiment (JSTAT) is a multi-disciplinary, peer-reviewed international journal created by the International School for Advanced Studies (SISSA) and IOP Publishing (IOP). JSTAT covers all aspects of statistical physics, including experimental work that impacts on the subject.
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Vincent D Blondel et al J. Stat. Mech. (2008) P10008
We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks.
Lucas Böttcher and Gregory Wheeler J. Stat. Mech. (2024) 023401
Analyzing the geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural-network structure, implementation attributes, and learning performance. In this paper, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the original space are rarely correctly identified as such in the expected lower-dimensional representations if random projections are used. The principal curvature in the expected lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature in random projections and mean curvature in the original space (i.e. the normalized Hessian trace) to compute Hutchinson-type trace estimates without calculating Hessian-vector products as in the original Hutchinson method. Because random projections are not suitable for correctly identifying saddle information, we propose to study projections along the dominant Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, for different common image classifiers and a function approximator, we show and compare random and Hessian projections of loss landscapes with up to approximately parameters.
Gernot Akemann et al J. Stat. Mech. (2024) 053501
The two-dimensional (2D) Coulomb gas is a one-parameter family of random point processes, depending on the inverse temperature β. Based on previous work, it is proposed as a simple statistical measure to quantify the intra- and interspecies repulsion among three different highly territorial birds of prey. Using data from the area of the Teutoburger Wald over 20 years, we fit the nearest-neighbour and next-to-nearest neighbour spacing distributions between the respective nests of the goshawk, eagle owl and the previously examined common buzzard to β of the Coulomb gas. Within each species, the repulsion measured in this way deviates significantly from the Poisson process of independent points in the plane. In contrast, the repulsion amongst each of two species is found to be considerably lower and closer to Poisson. Methodologically, we investigate the influence of the terrain, of a shorter interaction range given by the 2D Yukawa interaction, and the statistical independence of the time moving average we use for the yearly ensembles of occupied nests. We also check that an artificial random displacement of the original nest positions of the order of the mean level spacing quickly destroys the repulsion measured by β > 0. A simple, approximate analytical expression for the nearest-neighbour spacing distribution derived from non-Hermitian random matrix theory proves to be very useful.
Lorenzo Correale and Alessandro Silva J. Stat. Mech. (2024) 053101
We study the non-equilibrium phase diagram of a fully-connected Ising p-spin model, for generic p > 2, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range spin interaction. In particular, we investigate the dynamics of the mean-field model after a quantum quench: we observe a new dynamical phase transition which is either first or second order depending on the even or odd parity of p, in stark contrast with its thermal counterpart which is first order for all p. The dynamical phase diagram is qualitatively modified by the fluctuations introduced by a short-range interaction which drive the system always towards various prethermal paramagnetic phases determined by the strength of time dependent fluctuations of the magnetization.
Federico Corberi and Luca Smaldone J. Stat. Mech. (2024) 053204
We investigate the aging properties of the one-dimensional voter model with long-range interactions in its ordering kinetics. In this system, an agent, , positioned at a lattice vertex i, copies the state of another one located at a distance r, selected randomly with a probability . Employing both analytical and numerical methods, we compute the two-time correlation function () between the state of a variable Si at time s and that of another one, at distance r, at time t. At time t, the memory of an agent of its former state at time s, expressed by the autocorrelation function, decays algebraically for α > 1 as , where L is a time-increasing coherence length and λ is the Fisher–Huse exponent. We find λ = 1 for α > 2, and for . For , instead, there is an exponential decay, as in the mean field. Then, in contrast with what is known for the related Ising model, here we find that λ increases upon decreasing α. The space-dependent correlation obeys a scaling symmetry for α > 2. Similarly, for , one has , where the length regulating two-time correlations now differs from the coherence length as , with .
Maurizio Serva J. Stat. Mech. (2024) 053401
The particles that we describe here can only move at the speed of light c in three-dimensional space. The velocity, which randomly but continuously changes direction, can be represented as a point on the surface of a sphere of constant radius c, and its trajectories may only connect points of this variety. The Wiener process that we use to describe the velocity dynamics on the surface of the sphere is anisotropic since the infinitesimal variation of the velocity is not only always orthogonal to the velocity itself (which guarantees a constant speed), but also to the position. This choice for the infinitesimal variation of the velocity is the one that best slows down the diffusion of particles in space by random motion at the speed of light. As a result of these dynamics, the position of the particles spontaneously remain confined on the surface of an expanding sphere whose radius increases, for large times, as the square root of time.
Sourav Manna et al J. Stat. Mech. (2024) 053301
We study many-body localization in a hardcore boson model in the presence of random disorder on finite generation fractal lattices with different Hausdorff dimensions and different local lattice structures. In particular, we consider the Vicsek, T-shaped, Sierpinski gasket, and modified Koch-curve fractal lattices. In the single-particle case, these systems display Anderson localization for arbitrary disorder strength if they are large enough. In the many-body case, the systems available to exact diagonalization exhibit a transition between a delocalized and localized regime, visible in the spectral and entanglement properties of these systems. The position of this transition depends on the Hausdorff dimension of the given fractal, as well as on its local structure.
Tomoyuki Obuchi and Yoshiyuki Kabashima J. Stat. Mech. (2016) 053304
We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator (LASSO). First, on the basis of the message passing algorithm and a perturbative discussion assuming that the number of observations is sufficiently large, we provide simple formulas for approximately assessing two types of CV errors, which enable us to significantly reduce the necessary cost of computation. These formulas also provide a simple connection of the CV errors to the residual sums of squares between the reconstructed and the given measurements. Second, on the basis of this finding, we analytically evaluate the CV errors when the design matrix is given as a simple random matrix in the large size limit by using the replica method. Finally, these results are compared with those of numerical simulations on finite-size systems and are confirmed to be correct. We also apply the simple formulas of the first type of CV error to an actual dataset of the supernovae.
Jozef Sznajd J. Stat. Mech. (2024) 053202
Three 2D spin models made of frustrated zig-zag chains with competing interactions which, by exact summation with respect to some degrees of freedom, can be replaced by an effective temperature-dependent interaction, were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions, does not exhibit any finite temperature phase transition; nevertheless, temperature can trigger a frustration–no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models (Weiguo 2020 arXiv:2006.08921v2; 2020 2006.15087v1). The anisotropic Ising chains coupled by a direct interchain interaction and, competing with it, indirect interaction via spins located between chains, are analyzed using the exact Onsager's equation and linear perturbation renormalization group (LPRG). Depending on the parameter set, such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with a re-entrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial XXZ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model, for a certain set of parameters, the model can undergo three phase transitions. However, both intrachain and interchain plain interactions can eliminate the re-entrant disordered phase, and then only one transition takes place. Additionally, the XXZ model can undergo temperature-induced metamagnetic transition.
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Yao Xiao et al J. Stat. Mech. (2024) 063401
This study aims to investigate the behavioural evolution patterns of pedestrians who repeatedly traverse the same scenarios. To accomplish this objective, we implemented a repeated circle antipode experiment, ensuring consistent conditions for all participants. This experimental design allows for an effective examination of participant performance across multiple rounds. Our findings revealed that specific walking characteristics experienced significant changes with the progression of successive experiments, and participants demonstrated notable differences in their chosen routes. Recognizing the ability of the day-to-day dynamic model to describe the evolution of network flows and the similarities between traffic and pedestrian flows, we apply the modelling approach of the day-to-day dynamic model to the construction of pedestrian route choice modelling. Consequently, we developed a series of round-to-round pedestrian route choice models to characterize our experiment. These models factored in both historical walking experiences and the influence of neighbours. Our model proved to be reliable, achieving a route choice accuracy of approximately 80% in simulations of circle antipode experiments. The results of this study can provide valuable insights into pedestrian dynamics, aiding in understanding pedestrian behaviour during repetitive walking and facilitating the development of more accurate round-to-round route choice models.
Fabio Caceffo et al J. Stat. Mech. (2024) 063103
Recently, the entanglement asymmetry emerged as an informative tool to understand dynamical symmetry restoration in out-of-equilibrium quantum many-body systems after a quantum quench. For integrable systems the asymmetry can be understood in the space-time scaling limit via the quasiparticle picture, as it was pointed out in Ares et al (2023 Nat. Commun.14 2036) . However, a quasiparticle picture for quantum quenches from generic initial states was still lacking. Here we conjecture a full-fledged quasiparticle picture for the charged moments of the reduced density matrix, which are the main ingredients to construct the asymmetry. Our formula works for quenches producing entangled multiplets of an arbitrary number of excitations. We benchmark our results in the XX spin chain. First, by using an elementary approach based on the multidimensional stationary phase approximation we provide an ab initio rigorous derivation of the dynamics of the charged moments for the quench treated in Ares et al (2023 SciPost Phys.15 089). Then, we show that the same results can be straightforwardly obtained within our quasiparticle picture. As a byproduct of our analysis, we obtain a general criterion ensuring a vanishing entanglement asymmetry at long times. Next, by using the Lindblad master equation, we study the effect of gain and loss dissipation on the entanglement asymmetry. Specifically, we investigate the fate of the so-called quantum Mpemba effect (QME) in the presence of dissipation. We show that dissipation can induce QME even if unitary dynamics does not show it, and we provide a quasiparticle-based interpretation of the condition for the QME.
Federico Rottoli et al J. Stat. Mech. (2024) 063102
Entanglement Hamiltonians provide the most comprehensive characterisation of entanglement in extended quantum systems. A key result in unitary quantum field theories is the Bisognano-Wichmann theorem, which establishes the locality of the entanglement Hamiltonian. In this work, our focus is on the non-Hermitian Su-Schrieffer-Heeger (SSH) chain. We study the entanglement Hamiltonian both in a gapped phase and at criticality. In the gapped phase we find that the lattice entanglement Hamiltonian is compatible with a lattice Bisognano-Wichmann result, with an entanglement temperature linear in the lattice index. At the critical point, we identify a new imaginary chemical potential term absent in unitary models. This operator is responsible for the negative entanglement entropy observed in the non-Hermitian SSH chain at criticality.
Bishal Ghosh et al J. Stat. Mech. (2024) 063101
We investigate open quantum dynamics for a one-dimensional incommensurate Aubry–André–Harper lattice chain, a part of which is initially filled with electrons and is further connected to dephasing probes at the filled lattice sites. This setup is akin to a step-initial configuration where the non-zero part of the step is subjected to dephasing. We investigate the quantum dynamics of local electron density, the scaling of the density front as a function of time both inside and outside of the initial step, and the growth of the total number of electrons outside the step. We analyze these quantities in all three regimes, namely, the de-localized, critical, and localized phases of the underlying lattice. Outside the initial step, we observe that the density front spreads according to the underlying nature of single-particle states of the lattice, for both the de-localized and critical phases. For the localized phase, the spread of the density front hints at a logarithmic behavior in time that has no parallel in the isolated case (i.e. in the absence of probes). Inside the initial step, due to the presence of the probes, the density front spreads in a diffusive manner for all the phases. This combination of rich and different dynamical behavior, outside and inside the initial step, results in the emergence of mixed dynamical phases. While the total occupation of electrons remains conserved, the value outside or inside the initial step turns out to have a rich dynamical behavior. Our work is widely adaptable and has interesting consequences when disordered/quasi-disordered systems are subjected to a thermodynamically large number of probes.
Yusupjan Habibulla and Hai-Jun Zhou J. Stat. Mech. (2024) 063402
We study the minimum dominating set problem as a representative combinatorial optimization challenge with a global topological constraint. The requirement that the backbone induced by the vertices of a dominating set should be a connected subgraph makes the problem rather nontrivial to investigate by statistical physics methods. Here, we convert this global connectivity constraint into a set of local vertex constraints and build a spin glass model with only five coarse-grained vertex states. We derive a set of coarse-grained belief-propagation equations and obtain theoretical predictions of the relative sizes of the minimum dominating sets for regular random and Erdös–Rényi random graph ensembles. We also implement an efficient message-passing algorithm to construct close-to-minimum connected dominating sets and backbone subgraphs for single random graph instances. Our theoretical strategy may also be applicable to some other global topological constraints.
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Annabel L Davies and Tobias Galla J. Stat. Mech. (2022) 11R001
Network meta-analysis (NMA) is a technique used in medical statistics to combine evidence from multiple medical trials. NMA defines an inference and information processing problem on a network of treatment options and trials connecting the treatments. We believe that statistical physics can offer useful ideas and tools for this area, including from the theory of complex networks, stochastic modelling and simulation techniques. The lack of a unique source that would allow physicists to learn about NMA effectively is a barrier to this. In this article we aim to present the 'NMA problem' and existing approaches to it coherently and in a language accessible to statistical physicists. We also summarise existing points of contact between statistical physics and NMA, and describe our ideas of how physics might make a difference for NMA in the future. The overall goal of the article is to attract physicists to this interesting, timely and worthwhile field of research.
Shamik Gupta et al J. Stat. Mech. (2014) R08001
The phenomenon of spontaneous synchronization, particularly within the framework of the Kuramoto model, has been a subject of intense research over the years. The model comprises oscillators with distributed natural frequencies interacting through a mean-field coupling, and serves as a paradigm to study synchronization. In this review, we put forward a general framework in which we discuss in a unified way known results with more recent developments obtained for a generalized Kuramoto model that includes inertial effects and noise. We describe the model from a different perspective, highlighting the long-range nature of the interaction between the oscillators, and emphasizing the equilibrium and out-of-equilibrium aspects of its dynamics from a statistical physics point of view. In this review, we first introduce the model and discuss both for the noiseless and noisy dynamics and for unimodal frequency distributions the synchronization transition that occurs in the stationary state. We then introduce the generalized model, and analyze its dynamics using tools from statistical mechanics. In particular, we discuss its synchronization phase diagram for unimodal frequency distributions. Next, we describe deviations from the mean-field setting of the Kuramoto model. To this end, we consider the generalized Kuramoto dynamics on a one-dimensional periodic lattice on the sites of which the oscillators reside and interact with one another with a coupling that decays as an inverse power-law of their separation along the lattice. For two specific cases, namely, in the absence of noise and inertia, and in the case when the natural frequencies are the same for all the oscillators, we discuss how the long-time transition to synchrony is governed by the dynamics of the mean-field mode (zero Fourier mode) of the spatial distribution of the oscillator phases.
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Fabio Caceffo et al J. Stat. Mech. (2024) 063103
Recently, the entanglement asymmetry emerged as an informative tool to understand dynamical symmetry restoration in out-of-equilibrium quantum many-body systems after a quantum quench. For integrable systems the asymmetry can be understood in the space-time scaling limit via the quasiparticle picture, as it was pointed out in Ares et al (2023 Nat. Commun.14 2036) . However, a quasiparticle picture for quantum quenches from generic initial states was still lacking. Here we conjecture a full-fledged quasiparticle picture for the charged moments of the reduced density matrix, which are the main ingredients to construct the asymmetry. Our formula works for quenches producing entangled multiplets of an arbitrary number of excitations. We benchmark our results in the XX spin chain. First, by using an elementary approach based on the multidimensional stationary phase approximation we provide an ab initio rigorous derivation of the dynamics of the charged moments for the quench treated in Ares et al (2023 SciPost Phys.15 089). Then, we show that the same results can be straightforwardly obtained within our quasiparticle picture. As a byproduct of our analysis, we obtain a general criterion ensuring a vanishing entanglement asymmetry at long times. Next, by using the Lindblad master equation, we study the effect of gain and loss dissipation on the entanglement asymmetry. Specifically, we investigate the fate of the so-called quantum Mpemba effect (QME) in the presence of dissipation. We show that dissipation can induce QME even if unitary dynamics does not show it, and we provide a quasiparticle-based interpretation of the condition for the QME.
Federico Rottoli et al J. Stat. Mech. (2024) 063102
Entanglement Hamiltonians provide the most comprehensive characterisation of entanglement in extended quantum systems. A key result in unitary quantum field theories is the Bisognano-Wichmann theorem, which establishes the locality of the entanglement Hamiltonian. In this work, our focus is on the non-Hermitian Su-Schrieffer-Heeger (SSH) chain. We study the entanglement Hamiltonian both in a gapped phase and at criticality. In the gapped phase we find that the lattice entanglement Hamiltonian is compatible with a lattice Bisognano-Wichmann result, with an entanglement temperature linear in the lattice index. At the critical point, we identify a new imaginary chemical potential term absent in unitary models. This operator is responsible for the negative entanglement entropy observed in the non-Hermitian SSH chain at criticality.
Maurizio Serva J. Stat. Mech. (2024) 053401
The particles that we describe here can only move at the speed of light c in three-dimensional space. The velocity, which randomly but continuously changes direction, can be represented as a point on the surface of a sphere of constant radius c, and its trajectories may only connect points of this variety. The Wiener process that we use to describe the velocity dynamics on the surface of the sphere is anisotropic since the infinitesimal variation of the velocity is not only always orthogonal to the velocity itself (which guarantees a constant speed), but also to the position. This choice for the infinitesimal variation of the velocity is the one that best slows down the diffusion of particles in space by random motion at the speed of light. As a result of these dynamics, the position of the particles spontaneously remain confined on the surface of an expanding sphere whose radius increases, for large times, as the square root of time.
Federico Corberi and Luca Smaldone J. Stat. Mech. (2024) 053204
We investigate the aging properties of the one-dimensional voter model with long-range interactions in its ordering kinetics. In this system, an agent, , positioned at a lattice vertex i, copies the state of another one located at a distance r, selected randomly with a probability . Employing both analytical and numerical methods, we compute the two-time correlation function () between the state of a variable Si at time s and that of another one, at distance r, at time t. At time t, the memory of an agent of its former state at time s, expressed by the autocorrelation function, decays algebraically for α > 1 as , where L is a time-increasing coherence length and λ is the Fisher–Huse exponent. We find λ = 1 for α > 2, and for . For , instead, there is an exponential decay, as in the mean field. Then, in contrast with what is known for the related Ising model, here we find that λ increases upon decreasing α. The space-dependent correlation obeys a scaling symmetry for α > 2. Similarly, for , one has , where the length regulating two-time correlations now differs from the coherence length as , with .
Sourav Manna et al J. Stat. Mech. (2024) 053301
We study many-body localization in a hardcore boson model in the presence of random disorder on finite generation fractal lattices with different Hausdorff dimensions and different local lattice structures. In particular, we consider the Vicsek, T-shaped, Sierpinski gasket, and modified Koch-curve fractal lattices. In the single-particle case, these systems display Anderson localization for arbitrary disorder strength if they are large enough. In the many-body case, the systems available to exact diagonalization exhibit a transition between a delocalized and localized regime, visible in the spectral and entanglement properties of these systems. The position of this transition depends on the Hausdorff dimension of the given fractal, as well as on its local structure.
Lorenzo Correale and Alessandro Silva J. Stat. Mech. (2024) 053101
We study the non-equilibrium phase diagram of a fully-connected Ising p-spin model, for generic p > 2, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range spin interaction. In particular, we investigate the dynamics of the mean-field model after a quantum quench: we observe a new dynamical phase transition which is either first or second order depending on the even or odd parity of p, in stark contrast with its thermal counterpart which is first order for all p. The dynamical phase diagram is qualitatively modified by the fluctuations introduced by a short-range interaction which drive the system always towards various prethermal paramagnetic phases determined by the strength of time dependent fluctuations of the magnetization.
Gernot Akemann et al J. Stat. Mech. (2024) 053501
The two-dimensional (2D) Coulomb gas is a one-parameter family of random point processes, depending on the inverse temperature β. Based on previous work, it is proposed as a simple statistical measure to quantify the intra- and interspecies repulsion among three different highly territorial birds of prey. Using data from the area of the Teutoburger Wald over 20 years, we fit the nearest-neighbour and next-to-nearest neighbour spacing distributions between the respective nests of the goshawk, eagle owl and the previously examined common buzzard to β of the Coulomb gas. Within each species, the repulsion measured in this way deviates significantly from the Poisson process of independent points in the plane. In contrast, the repulsion amongst each of two species is found to be considerably lower and closer to Poisson. Methodologically, we investigate the influence of the terrain, of a shorter interaction range given by the 2D Yukawa interaction, and the statistical independence of the time moving average we use for the yearly ensembles of occupied nests. We also check that an artificial random displacement of the original nest positions of the order of the mean level spacing quickly destroys the repulsion measured by β > 0. A simple, approximate analytical expression for the nearest-neighbour spacing distribution derived from non-Hermitian random matrix theory proves to be very useful.
Jozef Sznajd J. Stat. Mech. (2024) 053202
Three 2D spin models made of frustrated zig-zag chains with competing interactions which, by exact summation with respect to some degrees of freedom, can be replaced by an effective temperature-dependent interaction, were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions, does not exhibit any finite temperature phase transition; nevertheless, temperature can trigger a frustration–no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models (Weiguo 2020 arXiv:2006.08921v2; 2020 2006.15087v1). The anisotropic Ising chains coupled by a direct interchain interaction and, competing with it, indirect interaction via spins located between chains, are analyzed using the exact Onsager's equation and linear perturbation renormalization group (LPRG). Depending on the parameter set, such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with a re-entrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial XXZ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model, for a certain set of parameters, the model can undergo three phase transitions. However, both intrachain and interchain plain interactions can eliminate the re-entrant disordered phase, and then only one transition takes place. Additionally, the XXZ model can undergo temperature-induced metamagnetic transition.
Bart Wijns et al J. Stat. Mech. (2024) 043203
A microscopic model for a translational Brownian motor, dubbed a Brownian translator, is introduced. It is inspired by the Brownian gyrator described by Filliger and Reimann (2007 Phys. Rev. Lett.99 230602). The Brownian translator consists of a spatially asymmetric object moving freely along a line due to perpetual collisions with a surrounding ideal gas. When this gas has an anisotropic temperature, both spatial and temporal symmetries are broken and the object acquires a nonzero drift. Onsager reciprocity implies the opposite phenomenon, that is dragging a spatially asymmetric object into an (initially at) equilibrium gas induces an energy flow that results in anisotropic gas temperatures. Expressions for the dynamical and energetic properties are derived as a series expansion in the mass ratio (of gas particle vs. object). These results are in excellent agreement with molecular dynamics simulations.
Vir B Bulchandani J. Stat. Mech. (2024) 043205
We point out that Percus's collision integral for one-dimensional hard rods (Percus 1969 Phys. Fluids12 1560–3) does not preserve the thermal equilibrium state in an external trapping potential. We derive a revised Enskog equation for hard rods and show that it preserves this thermal state exactly. In contrast to recent proposed kinetic equations for dynamics in integrability-breaking traps, both our kinetic equation and its thermal states are explicitly nonlocal in space. Our equation differs from earlier proposals at third order in spatial derivatives and we attribute this discrepancy to the choice of collision integral underlying our approach.