Finite-Size Effects in theφ4Field and Lattice Theory Above the Upper Critical Dimension

X. S. Chen () and V. Dohm
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X. S. Chen: Institut für Theoretische Physik, Technische Hochschule Aachen, D-52056, Aachen, Germany;
V. Dohm: Institut für Theoretische Physik, Technische Hochschule Aachen, D-52056, Aachen, Germany

International Journal of Modern Physics C (IJMPC), 1998, vol. 09, issue 07, 1007-1019

Abstract: We demonstrate that the standardO(n)symmetricφ4field theory does not correctly describe the leading finite-size effects near the critical point of spin systems with periodic boundary conditions on ad-dimensional lattice withd>4. We show that these finite-size effects require a description in terms of a lattice Hamiltonian. Forn →∞andn=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: Finite-Size Scaling; φ4Field Theory; Upper Critical Dimension; Five-Dimensional Ising Model; 05.70.Jk; 64.60.Ak; 75.40.Mg (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1142/S0129183198000947

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