Related papers: Effective ergodicity in single-spin-flip dynamics
We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates…
Monte Carlo simulations using entropic sampling to estimate the number of configurations of a given energy are a valuable alternative to traditional methods. We introduce {\it tomographic} entropic sampling, a scheme which uses multiple…
Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte-Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and…
We present highly accurate Monte Carlo results for simple cubic Ising lattices containing up to $256^3$ spins. These results were obtained by means of the Cluster Processor, a newly built special-purpose computer for the Wolff cluster…
We consider the single-spin-flip dynamics of the random-field Ising model on a Bethe lattice at zero temperature in the presence of a uniform external field. We determine the average magnetization as the external field is varied from minus…
We assess the ergodic properties of the Fermi-Pasta-Ulam-Tsingou-$\alpha$ model for generic initial conditions using a Toda integral. It serves as an adiabatic invariant for the system and a suitable observable to measure its equilibrium…
A mean-field model of Ising spin glass with the Hamiltonian being a sum of the infinite-range ferromagnetic and random antiferromagnetic interactions is studied. It is shown that this model has phase transition in external magnetic field…
The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for…
In this paper we establish new simple local geometric criteria for discrete entropic curvature introduced in [47] that are powerful enough to capture many geometric properties of complex models arising in mathematical physics. These results…
The two-dimensional Ising model on a distorted Kagom\'{e} lattice is studied by means of exact solutions and the tensor renormalisation group (TRG) method. The zero-field phase diagrams are obtained, where three phases such as…
We study a one-parameter family of interval maps $\{T_\alpha\}_{\alpha\in[1,\beta]}$, with $\beta$ the golden mean, defined on $[-1,1]$ by $T_\alpha(x)=\beta^{1+|t|}x-t\beta\alpha$ where $t\in\{-1,0,1\}$. For each $T_\alpha,\ \alpha>1$, we…
We report a metrology scheme which measures magnetic susceptibility of an atomic spin ensemble along the $x$ and $z$ direction and produces parameter estimation with precision beating the standard quantum limit. The atomic ensemble is…
The dynamic evolution at zero temperature of a uniform Ising ferromagnet on a square lattice is followed by Monte Carlo computer simulations. The system always eventually reaches a final, absorbing state, which sometimes coincides with a…
Extensive Monte Carlo study of two-dimensional Ising model is done to investigate the statistical behavior of spin clusters and interfaces as a function of temperature, $T$. We use a \emph{tie-breaking} rule to define interfaces of spin…
We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique…
Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo method with the appealing feature of being amenable to parallel computing. At each iteration, it samples several candidates for the next state of the Markov chain and…
We use quantum Monte Carlo methods and various analytic approximations to solve the Ising spin-glass model in a transverse field in the disordered phase. We focus on the behavior of the frequency dependent susceptibility of the system above…
We present the phase diagram, in both the microcanonical and the canonical ensemble, of the Self-Gravitating-Ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational…
Ergodicity sits at the heart of the connection between statistical mechanics and dynamics of a physical system. By fixing the initial state of the system into the ground state of the Hamiltonian at zero temperature and tuning a control…
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…