Finite size scaling of the correlation length above the upper critical dimension
Abstract
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.
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