Transfer matrix solution of the Ising model on the Koch curve

Abstract

A transfer matrix approach is used to calculate the partition function of the Ising model on the Koch curve. In zero magnetic field it is possible to obtain an exact analytic result. In the presence of a field the problem becomes more difficult. A procedure, based on an expansion about H = 0, is developed which shows that the spontaneous magnetisation vanishes identically and which makes it possible to give the zero field susceptibility as a power series in a small temperature dependent parameter.