Generalized boundary conditions for periodic lattice systems: application to the two-dimensional Ising model on a square lattice.
We show that the thermal properties of periodic lattice systems can be approximated to that of a finite cluster with appropriate boundary conditions which include a modified Hamiltonian for the boundary variables. Imposing lattice invariance on the correlation of the local site variables is sufficient to obtain the free parameters of the boundary Hamiltonian. The degree of accuracy of the calculation depends on the interaction range allowed in the boundary Hamiltonian and the range up to which the correlation of the site variables are made lattice invariant. The Bethe approximation can be considered a trivial case of this general method for clusters of one lattice site. The reliability of the method is demonstrated with the results obtained for the two-dimensional Ising model, where a cluster of four spins and invariance conditions up to second neighbors is sufficient to reproduce some nonuniversal thermal properties of the model with an accuracy comparable or better than other more complex numerical methods.
Etxebarria
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Fisika Aplikatua II Saila, Zientzia eta Teknologia Fakultatea, Euskal Herriko Unibertsitatea, P.K. 644, 48080 Bilbao, Spain. wmpetali@lg.ehu.es
Elcoro
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Perez-Mato
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