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 Tc, 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 Tc, 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 Tc. The boundary spontaneous magnetization approaches zero in the form of A(E′1)(1−T/Tc)1/2, and the boundary zero field magnetic susceptibility diverges at Tc in the form −B (E′1)ln|1−T/Tc|, where A(E′1) and B(E′) are increasing functions of E′1.