Finite-Size Scaling and Universality above the Upper Critical Dimensionality

Abstract

According to renormalization theory, Ising systems above their upper critical dimensionality $d_u=4\mathrm{}$ have classical critical behavior and the ratio of magnetization moments $Q=〈m^2{〉}^2/〈m^4〉$ has the universal value $0.456947\dots$. However, Monte Carlo simulations of $d=5\mathrm{}$ 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 $d_u<4\mathrm{}$, and a careful analysis of the corrections to scaling. Our results are in perfect agreement with the renormalization theory and provide an explanation of the discrepancy mentioned.