Finite-size scaling of the correlation length above the upper critical dimension in the five-dimensional Ising model

Abstract

We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size $L$ as ${L}^{5∕4}$, rather than proportional to $L$, as in standard finite-size scaling (FSS) theory. Our results confirm a hypothesis that FSS expressions in dimension $d$ greater than the upper critical dimension of 4 should have $L$ replaced by ${L}^{d∕4}$ for cubic samples with periodic boundary conditions. We also investigate numerically the logarithmic corrections to FSS in $d=4$.