Finite-Size Effects in the $φ^{4}$ Field Theory Above the Upper Critical Dimension

Details Finite-Size Effects in the $φ^{4}$ Field Theory Above the Upper Critical Dimension Finite-Size Effects in the $φ^{4}$ Field Theory Above the Upper Critical Dimension

1997-11-27

arxiv.org/abs/cond-mat/9711298v1

Int.J.Mod.Phys. C9 (1998) 1007-1019

Physics

Condensed Matter

4 pages, latex, 1 figure

Scientific paper

We demonstrate that the standard O(n) symmetric $\phi^{4}$ field theory does not correctly describe the leading finite-size effects near the critical point of spin systems 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 $n \to \infty$ and $n=1$ explicit results are given for the susceptibility and for the Binder cumulant. They imply that recent analyses of Monte-Carlo results for the five-dimensional Ising model are not conclusive.

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