Thermodynamics of an anisotropic boundary of a two-dimensional Ising model

Abstract

We consider a semi‐infinite two‐dimensional Ising model with its spins on the boundary row having a different interaction energy E′₁ from the ferromagnetic bulk. We find that the boundary specific heat has two divergent terms: one of which diverges linearly at the bulk critical temperature T_c, and the other, logaritmically. The linearly divergent term is independent of E′₁, and the coefficient of the logaritmically divergent term is a decreasing function of E′₁. There is a boundary latent heat at T_c, which is identical to McCoy and Wu's result. The boundary spins, which can be either ferromagnetic or antiferromagnetic, are aligned for temperature lower than T_c. The boundary spontaneous magnetization approaches zero in the form of A(E′₁)(1−T/T_c)^1/2, and the boundary zero field magnetic susceptibility diverges at T_c in the form −B (E′₁)ln|1−T/T_c|, where A(E′₁) and B(E′) are increasing functions of E′₁.