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On a variational procedure for obtaining the thermodynamic properties of statistical models
Author(s) -
Ferreira L. G.,
Salinas S. R.,
Oliveira M. J.
Publication year - 1977
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220830125
Subject(s) - hamiltonian (control theory) , ising model , coupling constant , heisenberg model , spin model , statistical physics , anisotropy , antiferromagnetism , mathematics , physics , quantum mechanics , mathematical optimization
A procedure is developed for obtaining approximate thermodynamic properties of statistical models, based on a well known variational principle for the free energy. The procedure involves the choice of a suitable parametrized trial Hamiltonian which contains some elementary interactions. The free trial Hamiltonian leads to the usual mean‐field approximation. When the trial Hamiltonian includes a certain number of pair interactions only, the results are regained of the constant‐coupling approximation for the Ising model if the number of interacting pairs is conveniently chosen by a comparison with the first few terms of the exact high‐temperature expansion. This procedure is simpler than existing approximations and can be easily generalized. Besides treating the Ising model, some applications are presented to the spin‐1/2 antiferromagnetic Heisenberg model, and to the spin‐1 Heisenberg model with uniaxial anisotropy.