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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 Tc are calculated. The critical exponent v 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 Tc 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. Non-perturbative aspects in the weak regime are analyzed and a singularity, of square root type, at zero vertical coupling is found. Also discussed is the transition from the weak to the strong vertical coupling regime and its physical manifestation through the rapidity with which the correlation length diverges at Tc.
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