Domain Walls and Shape Dependence in the Two-Dimensional Ising-Model Critical Region

Abstract

Ferdinand and Fisher have discovered some unusual lattice-shape effects on the finite-size-induced specific-heat peak shift in the two-dimensional Ising-model critical region. It is shown that they are well approximated by keeping only the two largest eigenvalues of the transfer matrix, and may be expressed entirely in terms of a one-dimensional Ising array of domain walls. Approximate expressions for the effective coupling and number of spins are given. It is also pointed out that in general domain walls should be thermodynamically important for such finite-size effects.