Critical temperature in 2D square Ising model with anisotropic coupling constant using Kramers-Wannier duality

Abstract

To solve the 2D square Ising model incorporating anisotropy, we discuss a graphical representation of Kramers-Wannier duality. The method yields an equation relating the critical temperature (Tc ) to the horizontal and vertical coupling constants. The result reproduces the known exact solution by Onsager. The equation derived was utilized to plot Tc as a function of anisotropy by introducing the ratio (α) of the coupling constants. A phase diagram is then obtained showing Tc as an increasing function of α In the limit as α approaches zero, the critical temperature asymptotically goes to zero. This agrees with the exact solution of the 1D model.