CONSTRUCTING THE CRITICAL CURVE FOR A SYMMETRIC TWO-LAYER ISING MODEL

Abstract

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 [Formula: see text], is obtained for very weak inter-layer interactions, ξ<0.1. Also a different function is given for the case of the strong inter-layer interactions (ξ>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 ϕ=γ is 1.74 for the system with the same intra-layer interaction and 0.5 for the system with different intra-layer interactions.