Finite-size Scaling and Universality above the Upper Critical Dimensionality

TL;DR

This paper confirms that above the upper critical dimension, Ising models exhibit classical critical behavior and resolves previous discrepancies through detailed simulations and analysis of scaling corrections.

Contribution

It demonstrates that the renormalization theory predictions hold above the upper critical dimension by analyzing a generalized model and correcting previous simulation discrepancies.

Findings

Results align with renormalization theory predictions

Discrepancies in earlier simulations are explained by scaling corrections

Monte Carlo simulations confirm classical critical behavior above d_u

Abstract

According to renormalization theory, Ising systems above their upper critical dimensionality d_u = 4 have classical critical behavior and the ratio of magnetization moments Q = <m^2>^2 / <m^4> has the universal value 0.456947... However, Monte Carlo simulations of d = 5 Ising models have been reported which yield strikingly different results, suggesting that the renormalization scenario is incorrect. We investigate this issue by simulation of a more general model in which d_u < 4, and a careful analysis of the corrections to scaling. Our results are in a perfect agreement with the renormalization theory and provide an explanation of the discrepancy mentioned.