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

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

2004-12-07

arxiv.org/abs/cond-mat/0412150v1

Phys. Rev. B71, 174438 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 6 postscript figures

Scientific paper

10.1103/PhysRevB.71.174438

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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