Two-dimensional Ising Model with Non-homogenous Interactions.

In this paper we investigate the Ising model on Z² with competing interactions. In this model we consider J1 as horizontal interactions and J₂ as vertical interactions where J₁,J₂ > 0. We prove that this model can reach a phase transition. Onsager considered the case where horizontal interaction parameter J1 and vertical interaction parameter J₂ are different. For any fixed J₁ and J₂, he showed that below a critical temperature Tc which depends on J₁ and J₂, phase transition occurs using some matrix transfer method. However in this paper we will prove the existence of phase transition using contours methods introduced by Sinai. We will show that there exists a ß₀ > 0 such that for ß > ß₀ there exist at least two limit Gibbs distribution which leads to the phenomena of phase transition. [ABSTRACT FROM AUTHOR]