Analysis of finite-size effect of infinite-range Ising model under Glauber dynamics

TL;DR

This paper investigates how finite system size influences the behavior of an infinite-range Ising model under Glauber dynamics, deriving differential equations to describe correlations and validating results with simulations.

Contribution

It introduces a perturbative approach to quantify finite-size effects and derives differential equations for correlation functions in the model.

Findings

Finite-size effects are characterized by O(1/N) perturbations.

Derived differential equations match simulation results.

Breakdown occurs near critical phenomena or magnetization reversal.

Abstract

We consider an infinite-range Ising model under the Glauber dynamics and determine the finite-size effect on the distribution of two spin variables as a perturbation of $O \left( 1/N \right)$. Based on several considerations, ordinary differential equations are derived for describing the time development of both a two-body correlation and the autocorrelation function of magnetization. The results of the calculation fit the simulation results, unless the perturbation theory breaks down because of critical phenomena or magnetization reversal.