Constructing the Critical Curve for a Symmetric Two-Layer Ising Model

Details Constructing the Critical Curve for a Symmetric Two-Layer Ising Model Constructing the Critical Curve for a Symmetric Two-Layer Ising Model

2004-06-27

arxiv.org/abs/cond-mat/0406664v1

J. Theo. Comp. Chem.Vol. 3, No. 2, 217-224(2004)

Physics

Condensed Matter

Statistical Mechanics

16 pages, 2 figures, 2tables

Scientific paper

A numerical method based on the transfer matrix method is developed to calculate the critical temperature of two-layer Ising ferromagnet with a weak inter-layer coupling. The reduced internal energy per site has been accurately calculated for symmetric ferromagnetic case, with the nearest neighbor coupling K1 = K2 = K (where K1 and K2 are the nearest neighbor interaction in the first and second layers, respectively) with inter layer coupling J. The critical temperature as a function of the inter-layer coupling J/K << 1, is obtained for very weak inter-layer interactions,J/K < 0.1 . Also a different function is given for the case of the strong inter-layer interactions (J/K > 1). The importance of these relations is due to the fact that there is no well tabulated data for the critical points versus J/K. We find the value of the shift exponent Phi = Gama is 1.74 for the system with the same intra-layer interaction and 0.5 for the system with different intra-layer interactions.

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