Scaling functions for systems with finite range of interaction

TL;DR

This paper numerically determines the universal scaling functions for magnetization, susceptibility, and Binder cumulant in two nonequilibrium models with variable interaction ranges, confirming universality and estimating long-range exponents.

Contribution

It provides the first detailed numerical analysis of the scaling functions for these models, demonstrating their universality and accurately estimating the decay exponents of critical amplitudes.

Findings

Scaling functions are universal across models and interaction ranges.

Long-range exponents are accurately estimated and consistent with Ising and classical universality classes.

Data collapse supports the universality hypothesis for these nonequilibrium systems.

Abstract

We present a numerical determination of the scaling functions of the magnetization, the suscep- tibility, and the Binders cumulant, for two nonequilibrium model systems with varying range of interactions. We consider Monte Carlo simulations of the block voter model (BVM) on square lat- tices and of the majority-vote model (MVM) on random graphs. In both cases, the satisfactory data collapse obtained for several system sizes and interaction ranges, supports the hypothesis that these functions are universal. Our analysis yields an accurate estimation of the long-range exponents, which govern the decay of the critical amplitudes with the range of interaction, and is consistent with the assumption that the static exponents are Ising-like for the BVM and classical for the MVM.