Extended scaling for ferromagnetic Ising models with zero-temperature transitions

TL;DR

This paper develops an extended scaling method for ferromagnetic Ising models with zero-temperature transitions, enabling accurate data scaling across all temperatures in one- and two-dimensional models.

Contribution

It introduces a new scaling variable inspired by high-temperature series expansions, extending the applicability of scaling methods to models with zero-temperature critical points.

Findings

Successful scaling of 1D Ising ferromagnet data across all temperatures

Excellent finite-size scaling in 2D fully frustrated Villain model

Broadened the scope of extended scaling methods to zero-temperature transitions

Abstract

We study the second-moment correlation length and the reduced susceptibility of two ferromagnetic Ising models with zero-temperature ordering. By introducing a scaling variable motivated by high-temperature series expansions, we are able to scale data for the one-dimensional Ising ferromagnet rigorously over the entire temperature range. Analogous scaling expressions are then applied to the two-dimensional fully frustrated Villain model where excellent finite-size scaling over the entire temperature range is achieved. Thus we broaden the applicability of the extended scaling method to Ising systems having a zero-temperature critical point.