Journal of Physics A Mathematical and General

Constrained variational approach to second order phase transitions: application to a two-layer Ising film

Leonardo Angelini, D. Caroppo, M. Pellicoro, M Villani

Published Nov 7, 1992• 13 citations

Abstract

Within the framework of the transfer matrix formalism, a variational method is elaborated with a constraint related to the fundamental role of the correlation length near a critical point. The method is applied to a two-layer ferromagnetic film, made of two horizontal Ising planes interacting through a vertical coupling. The critical curve of the model, as well as the correlation length above and near T c are calculated. The critical exponent nu obtained agrees with the expected two-dimensional exact value. For the two particular values of the vertical coupling, for which there are numerical estimates of T c through series analysis or the Monte Carlo method, an essential agreement with these estimates is found. Analytical expressions are given in the weak and strong vertical coupling regimes.

DOI: 10.1088/0305-4470/25/21/006

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