相关论文: A Spectral Condition for Spectral Gap: Fast Mixing…
We construct a parallel stochastic dynamics with invariant measure converging to the Gibbs measure of the low temperature Ising model. The proof of such convergence requires a polymer expansion based on suitably defined Peierls-type…
Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. Applications include Markov Chain Monte Carlo (MCMC) simulation and distributed scheduling for wireless networks. In…
We consider an equilibrium birth and death type process for a particle system in infinite volume, the latter is described by the space of all locally finite point configurations on $\R^d$. These Glauber type dynamics are Markov processes…
We discuss the eigenvalue spacing statistics of the Glauber matrix for various models of statistical mechanics (a one dimensional Ising model, a two dimensional Ising model, a one dimensional model with a disordered ground state, and a SK…
We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of…
We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We…
A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($T_{o}$). Detailed balance is violated so that the spin…
This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular…
In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincar\'{e} inequality) and the transportation inequality for Gibbs measures, under the Dobrushin uniqueness condition. Moreover, we give a generalization of…
The Glauber model is reconsidered based on a quantum formulation of the Master equation. Unlike the conventional approach the temperature and the Ising energy are included from the beginning by introducing a Heisenberg-like picture of the…
It is analytically shown that the one-dimensional Ising model with Glauber dynamics exhibits short time memory effects when submitted to an abrupt change in the temperature. These effects are qualitatively similar to those experimentally…
In this work we performed numerical simulations for the Ising model on three dimensional lattices with coordination number equal 5. With Monte Carlo simulations in the static case we evaluated the critical temperature and the static…
We investigate the limit behaviour of the spectral measures of matrices following the Gibbs measure for the Ising model on random graphs, Potts model on random graphs, matrices coupled in a chain model or induced QCD model. For most of…
This paper provides an overview of the research on the metastable behavior of the Ising model. We analyze the transition times from the set of metastable states to the set of the stable states by identifying the critical configurations that…
We weaken the assumption of summable variations in a paper by Verbitskiy \cite{verb} to a weaker condition, Berbee's condition, in order for a 1-block factor (a single site renormalisation) of the full shift space on finitely many symbols…
The Ising-Kac model is a variant of the ferromagnetic Ising model in which each spin variable interacts with all spins in a neighbourhood of radius $\gamma^{-1}$ for $\gamma \ll 1$ around its base point. We study the Glauber dynamics for…
We develop a renormalisation group approach to deriving the asymptotics of the spectral gap of the generator of Glauber type dynamics of spin systems with strong correlations (at and near a critical point). In our approach, we derive a…
We study the dynamical behavior of a square lattice Ising model with exchange and dipolar interactions by means of Monte Carlo simulations. After a sudden quench to low temperatures we find that the system may undergo a coarsening process…
We study Glauber dynamics for sampling from discrete distributions $\mu$ on the hypercube $\{\pm 1\}^n$. Recently, techniques based on spectral independence have successfully yielded optimal $O(n)$ relaxation times for a host of different…
We consider general mixed $p$-spin mean field spin glass models and provide a method to prove that the spectral gap of the Dirichlet form associated with the Gibbs measure is of order one at sufficiently high temperature. Our proof is based…