Extended Scaling in High Dimensions

TL;DR

This paper demonstrates that extended scaling significantly broadens the high-temperature critical regime in high-dimensional Ising models, enabling precise measurement of critical parameters through Monte Carlo simulations.

Contribution

It applies and validates the extended scaling scheme to high-dimensional Ising systems, improving the accuracy of critical parameter estimation.

Findings

Extended scaling broadens the critical regime in high-dimensional Ising models.

Accurate determination of critical temperatures and scaling indices is achieved.

Monte Carlo simulations confirm the effectiveness of extended scaling.

Abstract

We apply and test the recently proposed "extended scaling" scheme in an analysis of the magnetic susceptibility of Ising systems above the upper critical dimension. The data are obtained by Monte Carlo simulations using both the conventional Wolff cluster algorithm and the Prokof'ev-Svistunov worm algorithm. As already observed for other models, extended scaling is shown to extend the high-temperature critical scaling regime over a range of temperatures much wider than that achieved conventionally. It allows for an accurate determination of leading and sub-leading scaling indices, critical temperatures and amplitudes of the confluent corrections.