Specific Heat of Ising Model with Holes: Mathematical Details Using Dimer Approaches

Abstract

In this paper, we use the dimer method to obtain the free energy of Ising models consisting of repeated horizontal strips of width m connected by sequences of vertical strings of length n mutually separated by distance N , with N arbitrary, to investigate the effects of connectivity and proximity on the specific heat. The decoration method is used to transform the strings of n + 1 spins interacting with their nearest neighbors with coupling J into a pair with coupling Ĵ between the two spins. The free energy per site is given as a single integral and some results for critical temperatures are derived.