Finite-Size Scaling at Phase Coexistence

TL;DR

This paper develops a finite-size scaling theory for moments of the order parameter at phase coexistence, providing methods for analyzing numerical simulations and testing them on the 2D Ising model.

Contribution

It introduces a finite-size scaling framework for moments of the order parameter at phase coexistence and proposes practical analysis methods for numerical data.

Findings

FSS for low-order moments is complete under certain assumptions.

Numerical tests confirm the validity of the proposed scaling methods.

Application to the 2D Ising model demonstrates practical usefulness.

Abstract

{}From a finite-size scaling (FSS) theory of cumulants of the order parameter at phase coexistence points, we reconstruct the scaling of the moments. Assuming that the cumulants allow a reconstruction of the free energy density no better than as an asymptotic expansion, we find that FSS for moments of low order is still complete. We suggest ways of using this theory for the analysis of numerical simulations. We test these methods numerically through the scaling of cumulants and moments of the magnetization in the low-temperature phase of the two-dimensional Ising model. (LaTeX file; ps figures included as shar file)