The Ising universality class in dimension three: corrections to scaling

TL;DR

This study analyzes corrections to scaling in four three-dimensional Ising models, confirming the universal ratio of correction amplitudes and identifying a subleading correction exponent consistent with theoretical predictions.

Contribution

It provides the first comprehensive estimation of corrections to scaling across multiple 3D Ising models, confirming universality and the presence of a specific subleading correction exponent.

Findings

A correction term with an exponent consistent with $ heta_{2} \\sim 2.454(3)$ is almost always present.

The normalized Binder cumulant shows zero amplitude for the leading confluent correction.

The universal ratio of correction amplitudes $a_{\\chi_{4}}/a_{\\chi} = 2$ is confirmed.

Abstract

Simulation data are analyzed for four 3D spin-$1/2$ Ising models: on the FCC lattice, the BCC lattice, the SC lattice and the Diamond lattice. The observables studied are the susceptibility, the reduced second moment correlation length, and the normalized Binder cumulant. From measurements covering the entire paramagnetic temperature regime the corrections to scaling are estimated. We conclude that a correction term having an exponent which is consistent within the statistics with the bootstrap value of the universal subleading thermal confluent correction exponent, $\theta_{2} \sim 2.454(3)$, is almost always present with a significant amplitude. In all four models, for the normalized Binder cumulant the leading confluent correction term has zero amplitude. This implies that the universal ratio of leading confluent correction amplitudes $a_{\chi_{4}}/a_{\chi} = 2$ in the 3D Ising universality class.