Finite-Size Scaling on the Ising Coexistence Line

TL;DR

This paper tests finite-size scaling theories in the low-temperature phase of the 2D Ising model, confirming some predictions while highlighting issues with existing approaches regarding free energy convexity.

Contribution

It evaluates the validity of Borgs and Kotecký's finite-size scaling ansatzes for magnetisation moments in the 2D Ising model's low-temperature phase.

Findings

Good agreement with Borgs and Kotecký's ansatz for magnetisation moments

Identifies inadequacies in current approaches concerning free energy convexity

Highlights the importance of free energy convexity in finite-size scaling

Abstract

We report tests of finite-size scaling ansatzes in the low temperature phase of the two-dimensional Ising model. For moments of the magnetisation density, we find good agreement with the new ansatz of Borgs and Koteck\'y, and clear evi consequences of the convexity of the free energy are not adequately treated in either of these approaches.\lb {\it Keywords}\/: Finite-size scaling, 2-d Ising, pure-phase susceptibility.