The crossover from first to second-order finite size scaling: A numerical study Christian Borgs

TL;DR

This study investigates finite-size scaling behavior in a specific two-dimensional model during a first-order phase transition, confirming theoretical predictions and revealing a universal scaling curve near criticality.

Contribution

It provides numerical evidence for the crossover from first to second-order finite size scaling in a non-symmetric first-order transition.

Findings

Verification of asymptotic predictions by Borgs and Kotecky

Data collapse onto a universal curve near critical temperature

Rescaling system size by correlation length reveals universal behavior

Abstract

We consider a particular case of the two dimensional Blume-Emery-Griffiths model to study the finite-size scaling for a field driven first-order phase transition with two coexisting phases not related by a symmetry. For low temperatures we verify the asymptotic (large volume) predictions of the rigorous theory of Borgs and Kotecky, including the predictions concerning the so-called equal-weight versus equal-height controversy. Near the critical temperature we show that all data fit onto a unique curve, even when the correlation length xi becomes comparable to or larger then the size of the system, provided the linear dimension L of the system is rescaled by xi.