Journal of Statistical Physics最新文献

We address the problem of stability of one-dimensional non-periodic ground-state configurations in classical lattice-gas models with respect to finite-range perturbations of interactions. We show that a relevant property of ground-state configurations in this context is their homogeneity. The so-called strict boundary condition says that the number of finite patterns of a configuration has bounded fluctuations uniform in any finite subset of the lattice (mathbb Z). We show that if the strict boundary condition is not satisfied and interactions between particles decay at least as fast as (1/r^{alpha }) with (alpha >2), then ground-state configurations are not stable. In the Thue–Morse ground state, the number of finite patterns may fluctuate as much as the logarithm of the length of a lattice subset. We show that the Thue–Morse ground state is unstable for any (alpha >1) with respect to arbitrarily small two-body interactions favoring the presence of molecules consisting of two neighboring up or down spins. We also investigate Sturmian systems defined by irrational rotations on the circle. They satisfy the strict boundary condition but nevertheless they are unstable for (alpha >3).

We study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on N annuli of radii of the order of (r_0) and thickness (varepsilon ). We prove that when (r_0= |log varepsilon |^alpha ), (alpha >1), the vorticity field of the fluid converges for (varepsilon rightarrow 0) to the point vortex model, in an interval of time which diverges as (log |log varepsilon |). This generalizes previous result by Cavallaro and Marchioro in (J Math Phys 62:053102, 2021), that assumed (alpha >2) and in which the convergence was proved for short times only.

In this paper, we study a mean-field spin model with three- and two-body interactions. In a recent paper (Ann Henri Poincaré, 2024) by Contucci, Mingione and Osabutey, the equilibrium measure for large volumes was shown to have three pure states, two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. The authors proved a central limit theorem for the suitably rescaled magnetization. The aim of our paper is presenting a prove of a central limit theorem for the rescaled magnetization applying the exchangeable pair approach due to Stein. Moreover we prove (non-uniform) Berry–Esseen bounds, a concentration inequality, Cramér-type moderate deviations and a moderate deviations principle for the suitably rescaled magnetization. Interestingly we analyze Berry–Esseen bounds in case the model-parameters ((K_n,J_n)) converge to the critical point (0, 1) on lines with different slopes and with a certain speed, and obtain new limiting distributions and thresholds for the speed of convergence.

We consider the diluted multi-species Sherrington–Kirkpatrick (DMSK) model in which the variance of disorders depend on the species the particles belong to, and the number of edges within each block is diluted. First, we find the annealed region of the DMSK model at high temperature and compute the corresponding free energy. Next, we get a fluctuation result for the overlap vector through a differential method. Lastly, by using cavity method, we obtain the corresponding replica symmetric bound and r-step of replica symmetry breaking bound.

We study a hierarchical model of non-overlapping cubes of sidelengths (2^j), (jin {mathbb {Z}}). The model allows for cubes of arbitrarily small size and the activities need not be translationally invariant. It can also be recast as a spin system on a tree with a long-range hard-core interaction. We prove necessary and sufficient conditions for the existence and uniqueness of Gibbs measures, discuss fragmentation and condensation, and prove bounds on the decay of two-point correlation functions.

This paper is devoted to investigating Freidlin–Wentzell’s large deviation principle for one (spatial) dimensional nonlinear stochastic wave equation (frac{partial ^2 u^{{varepsilon }}(t,x)}{partial t^2}=frac{partial ^2 u^{{varepsilon }}(t,x)}{partial x^2}+sqrt{{varepsilon }}sigma (t, x, u^{{varepsilon }}(t,x))dot{W}(t,x)), where (dot{W}) is white in time and fractional in space with Hurst parameter (Hin big (frac{1}{4},frac{1}{2}big )). The variational framework and the modified weak convergence criterion proposed by Matoussi et al. (Appl Math Optim 83(2):849–879, 2021) are adopted here.

The discrete nonlinear Schrödinger equation on ({mathbb Z}^d), (d ge 1) is an example of a dispersive nonlinear wave system. Being a Hamiltonian system that conserves also the (ell ^2({mathbb Z}^d))-norm, the well-posedness of the corresponding Cauchy problem follows for square-summable initial data. In this paper, we prove that the well-posedness continues to hold for initial data that can grow towards infinity, namely anything that has at most a certain power law growth far away from the origin. The growth condition is loose enough to guarantee that, at least in dimension (d=1), initial data sampled from any reasonable equilibrium distribution of the defocusing DNLS satisfies it almost surely.

In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov–Poisson equation, in the regime where the solutions have bounded densities. We combine Golse and Paul’s method from [Arch Ration Mech Anal 223:57–94, 2017], which uses a semiclassical version of the optimal transport distance and which was adapted to the case of the Coulomb and gravitational interactions by the second author in [J Stat Phys 177:20–60, 2019], with a new approach developed by the first author in [Arch Ration Mech Anal 244:27–50, 2022] to quantitatively improve stability estimates in kinetic theory.

The purpose of this note is to consider a number of straightforward generalizations of the Pirogov–Sinai theory which can be covered by minor additions to the canonical texts. These generalizations are well-known among the adepts of the Pirogov–Sinai theory but are lacking formal references.

In this article we study the dynamics of one-dimensional relativistic billiards containing particles with positive and negative energy. We study configurations with two identical positive masses and symmetric positions with two massless particles between them of negative energy and symmetric positions. We show that such systems have finitely many collisions in any finite time interval. This is due to a phenomenon we call tachyonic collision, which occur at small scales and produce changes in the sign of the energy of individual particles. We also show that depending on the initial parameters the solutions can be bounded with certain periodicity or unbounded while obeying an inverse square law at large distances.