Theory of a Two-Dimensional Ising Model with Random Impurities. I. Thermodynamics

Recent experiments demonstrate that at the Curie temperature the specific heat may be a smooth function of the temperature. We propose that this effect can be due to random impurities and substantiate our proposal by a study of an Ising model containing such impurities. We modify the usual rectangular lattice by allowing each row of vertical bonds to vary randomly from row to row with a prescribed probability function. In the case that this probability is a particular distribution with a narrow width, we find that the logarithmic singularity of Onsager's lattice is smoothed out into a function which at $T_c$ is infinitely differentiable but not analytic. This function is expressible in terms of an integral involving Bessel functions and is computed numerically.