Relaxation time is monotone in temperature in the mean-field Ising model

TL;DR

This paper proves that in the mean-field Ising model with Glauber dynamics, the relaxation time decreases monotonically as temperature increases, providing insights into the system's thermal behavior.

Contribution

It establishes the monotonic relationship between relaxation time and temperature in the mean-field Ising model, a result not previously demonstrated.

Findings

Relaxation time decreases with increasing temperature.

Monotonic relationship holds for the mean-field Ising model.

Provides theoretical proof for the temperature dependence of relaxation time.

Abstract

In this note we consider the Glauber dynamics for the mean-field Ising model, when all couplings are equal and the external field is uniform. It is proved that the relaxation time of the dynamics is monotonically decreasing in temperature.