Related papers: Optimality of Glauber dynamics for general-purpose…
Consider Glauber dynamics for the Ising model on a graph of $n$ vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least $n\log n/f(\Delta)$, where $\Delta$ is the maximum degree and $f(\Delta) = \Theta(\Delta…
We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie-Weiss Model. For beta < 1, we prove that the dynamics exhibits a cut-off: the distance to stationarity drops from near 1 to near 0 in a window…
We present novel results for fast mixing of Glauber dynamics using the newly introduced and powerful Spectral Independence method from [Anari, Liu, Oveis-Gharan: FOCS 2020]. We mainly focus on the Hard-core model and the Ising model. We…
We prove an optimal $O(n \log n)$ mixing time of the Glauber dynamics for the Ising models with edge activity $\beta \in \left(\frac{\Delta-2}{\Delta}, \frac{\Delta}{\Delta-2}\right)$. This mixing time bound holds even if the maximum degree…
We consider Glauber dynamics of classical spin systems of Ising type in the limit when the temperature tends to zero in finite volume. We show that information on the structure of the most profound minima and the connecting saddle points of…
Large interacting systems in biology often exhibit emergent dynamics, such as coexistence of multiple time scales, manifested by fat tails in the distribution of waiting times. While existing tools in statistical inference, such as maximum…
We consider the phase ordering problem for the low-temperature Ising dynamics initialized from a biased and disordered initialization. Work of Fontes, Schonmann, Sidoravicius (2002) showed that at zero-temperature, Ising Glauber dynamics on…
We introduce a new framework for analyzing Glauber dynamics for the Ising model. The traditional approach for obtaining sharp mixing results has been to appeal to estimates on spatial properties of the stationary measure from within a…
Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…
We study zero-temperature Glauber dynamics for Ising-like spin variable models in quenched random networks with random zero-magnetization initial conditions. In particular, we focus on the absorbing states of finite systems. While it has…
We use Glauber dynamics to study frequency and temperature dependence of hysteresis loops in the pure (without quenched disorder) Ising model on cubic, square, honeycomb lattices and random graphs. Results are discussed in the context of…
We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm of the…
Continuum Glauber dynamics is a spatial birth-death process whose stationary distribution is a Gibbs distribution. We establish a spectral gap for Continuum Glauber dynamics applied to Gibbs point processes with repulsive pair potentials, a…
In this paper, we present a novel extension to the classical path coupling method to statistical mechanical models which we refer to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path…
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…
In VLSI physical design, many algorithms require the solution of difficult combinatorial optimization problems such as max/min-cut, max-flow problems etc. Due to the vast number of elements typically found in this problem domain, these…
Sampling Gibbs measures at low temperatures is an important task but computationally challenging. Numerical evidence suggests that the infinite-swapping algorithm (isa) is a promising method. The isa can be seen as an improvement of the…
Motivated by recent numerical findings [M. Henkel, T. Enss, and M. Pleimling, J. Phys. A: Math. Gen. 39 (2006) L589] we re-examine via Monte Carlo simulations the linear response function of the two-dimensional Ising model with Glauber…
Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the…
We analyse the metastable behaviour of the dilute Curie-Weiss model subject to a Glauber dynamics. The model is a random version of a mean-field Ising model, where the coupling coefficients are Bernoulli random variables with mean $p\in…