Finite-Size Effects in the φ4 Field and Lattice Theory Above the Upper Critical Dimension
- 1 October 1998
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Modern Physics C
- Vol. 09 (07) , 1007-1019
- https://doi.org/10.1142/s0129183198000947
Abstract
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.Keywords
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