Related papers: Low-temperature Ising dynamics with random initial…
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…
We consider time evolution in models close to integrable points with hidden symmetries that generate infinitely many local conservation laws that do not commute with one another. The system is expected to (locally) relax to a thermal…
We consider the long-ranged Ising spin-glass with random couplings decaying as a power-law of the distance, in the region of parameters where the spin-glass phase exists with a positive droplet exponent. For the Metropolis single-spin-flip…
We use zero-temperature Glauber dynamics to study hysteresis in the random-field Ising model on directed random graphs. The critical behavior of the model depends on the connectivity $z$ of the graph rather differently from that on…
The infinite-volume limit behavior of the 2d Ising model under possibly strong random boundary conditions is studied. The model exhibits chaotic size-dependence at low temperatures and we prove that the `+' and `-' phases are the only…
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…
The Wolff dynamics is a non-local Markov chain widely used for simulating the Ising model due to its effectiveness in reducing critical slowing down compared to the Glauber dynamics. Despite extensive algorithmic and numerical studies, a…
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…
This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions interactions arise naturally in several…
We study the evolution of spin clusters on two dimensional slices of the $3d$ Ising model in contact with a heat bath after a sudden quench to a subcritical temperature. We analyze the evolution of some simple initial configurations, such…
The Glauber model on a one-dimensional lattice with boundaries (for the ferromagnetic- and anti-ferromagnetic case) is considered. The large-time behaviour of the one-point function is studied. It is shown that, for any positive…
Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator…
Explicit relations between the isospin mixing probability, the spreading width $\Gamma_{IAS}^{\downarrow}$ of the Isobaric Analog State (IAS) and the statistical decay width $\Gamma_c$ of the compound nucleus at finite excitation energy,…
The magnetic properties of a nonequilibrium spin-1/2 cylindrical Ising nanowire system with core/shell in an oscillating magnetic field are studied by using a mean-field approach based on the Glauber-type stochastic dynamics (DMFT). We…
In this article, we review the metastable hierarchy in low-temperature lattice models. In the first part, we state that for any abstract lattice system governed by a Hamiltonian potential and evolving according to a Metropolis-type…
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\beta_s(q)$ strictly lower than the critical $\beta_c(q)$ for uniqueness…
We investigate low temperature properties of a random Ising model with $+J$ and $-aJ (a \neq 1)$ bonds in two dimensions using a cluster heat bath method. It is found that the Binder parameters $g_L$ for different sizes of the lattice come…
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo…
We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising models with edge activities $\boldsymbol{\beta} > 1$ and external fields $\boldsymbol{\lambda}<1$ (or symmetrically, $\boldsymbol{\lambda}>1$) on…
We investigate the Langevin dynamics for Wigner matrices with a spherical spike, in the regime where the signal-to-noise ratio $\theta$ is large, but order one. For large, order-$1$, signal-to-noise, the (worst-case) mixing time undergoes a…