Scaling above the upper critical dimension in Ising Models

TL;DR

This paper revisits finite size scaling in high-dimensional Ising models, deriving formulas via Mean Field Theory and confirming predictions through numerical simulations in five dimensions.

Contribution

It provides a new derivation of finite size scaling formulas above the upper critical dimension using Mean Field Theory and validates them with numerical simulations.

Findings

Numerical data agree with Mean Field predictions

Finite size exponent of connected susceptibility confirmed

Binder cumulant value matches theoretical predictions

Abstract

We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our numerical data are in a good agreement with the Mean Field theoretical predictions, in particular, with the finite size exponent of the connected susceptibility and with the value of the Binder cumulant.