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

We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size L as L5∕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 Ld∕4 for cubic samples with periodic boundary conditions. We also investigate numerically the logarithmic corrections to FSS in $d=4$.