An Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses

TL;DR

This paper introduces an extended scaling scheme for ferromagnets and spin glasses that improves the analysis of thermodynamic observables over a wider temperature range, enhancing the accuracy of critical parameter estimates.

Contribution

It proposes a new extended scaling scheme based on high temperature series expansions that better captures temperature and system size dependencies.

Findings

The extended scaling scheme aligns well with data from 2d ferromagnets and 3d spin glasses.

It provides consistent estimates of critical parameters across different observables.

The scheme broadens the effective temperature range for scaling analysis.

Abstract

From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scaling scheme involving a set of scaling formulae which express to leading order the temperature (T) and the system size (L) dependences of thermodynamic observables over a much wider range of T than the corresponding one in the conventional scaling scheme. The extended scaling, illustrated by data on the canonical 2d ferromagnet and on the 3d binomial Ising spin glass, leads to consistency for the estimates of critical parameters obtained from scaling analyses for different observables.