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 $d=4$ .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 $d=4$.

arXiv:cond-mat/0412150Physical Review BMay 31, 200551 citations

Scaling Theory for Finite-Size Effects in the Critical Region

Michael Ellis Fisher, Michael N. Barber

Current physics sources and commentsJan 1, 19882 citations

We show numerically that correlation length at the critical point in the five-dimensional Ising model varies with system size

L

{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