Residual entropy of the square Ising antiferromagnet in the maximum critical field: The Fibonacci matrix

Abstract

We find the analytical expression for the residual entropy of the square Ising model with nearest-neighbour antiferromagnetic coupling J, in the maximum critical field H-c = 4J, in terms of the Fibonacci matrix, which itself represents a self-similar, fractal object. The result coincides with the existing numerical data. By considering regular self-similar fractal objects rather than seemingly random transfer matrices, this approach opens the possibility of finding the corresponding solutions in more complicated cases, such as the antiferromagnets with longer than nearest-neighbour interactions and the three-dimensional antiferromagnets, as well as the possibility of unification of results pertinent to different lattices in two and three dimensions.