Limit Profile for the high-temperature Curie-Weiss model

TL;DR

This paper analyzes the high-temperature behavior of the Glauber dynamics in the Curie-Weiss model, revealing a near-deterministic evolution followed by diffusion near the cutoff, advancing understanding of phase transition dynamics.

Contribution

It introduces a novel two-dimensional approach to describe the limit profile of Glauber dynamics in the Curie-Weiss model at high temperature.

Findings

Near-deterministic evolution before cutoff

Diffusion approximation after cutoff

Extension of methods from Bernoulli-Laplace urns

Abstract

In this paper, we consider the Ising model on the complete graph, also known as the Curie-Weiss model, and establish the limit profile of the Glauber dynamics in the high-temperature regime. Our strategy is a two-dimensional analog of the method developed by Olesker-Taylor and Schmid for the Bernoulli-Laplace urn: The two-coordinate chain associated to the model evolves near-deterministically until just before the cutoff window, while afterwards it approximates a two-dimensional diffusion.