We demonstrate that the standard O(n) symmetric φ4 field theory does not correctly describe the leading finite-size effects near the critical point of spin systems with periodic boundary conditions on a d-dimensional lattice with d>4. We show that these finite-size effects require a description in terms of a lattice Hamiltonian. For n →∞ and n=1, explicit results are given for the susceptibility and for the Binder cumulant. They imply that these quantities do not have the universal properties predicted previously and that recent analyses of Monte Carlo results for the five-dimensional Ising model are not conclusive.We demonstrate that the standard O(n) symmetric φ4 field theory does not correctly describe the leading finite-size effects near the critical point of spin systems with periodic boundary conditions on a d-dimensional lattice with d>4. We show that these finite-size effects require a description in terms of a lattice Hamiltonian. For n →∞ and n=1, explicit results are given for the susceptibility and for the Binder cumulant. They imply that these quantities do not have the universal properties predicted previously and that recent analyses of Monte Carlo results for the five-dimensional Ising model are not conclusive.

arXiv:cond-mat/9711298International Journal of Modern Physics COct 1, 199817 citations

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

Jeff L. Jones, A. P. Young

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

Finite-Size Effects of the One-Dimensional Ising Model

L. S. Ferreira, J. A. Plascak

Brazilian Journal of PhysicsApr 13, 20235 citations

Finite-size effects in the quasi-two-dimensional Ising model

Atsushi Yamagata

Physica A Statistical Mechanics and its ApplicationsApr 1, 19945 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