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

Jeff L. Jones·A. P. Young
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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.

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Jeff L. Jones, A. P. Young. 2004-12-07. Finite size scaling of the correlation length above the upper critical dimension. https://doi.org/10.1103/physrevb.71.174438

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