Residual entropies of the Ising antiferromagnets on fractals: I. d-dimensional sierpinski gasket type of fractals

Abstract

We apply a new method to study the problem of the residual entropies of the antiferromagnetic Ising systems, in the maximum critical field, situated on Sierpinski gasket (SG) type of fractal lattices. The SG fractal lattices comprise a family, so that each member is labelled by an integer b (2⪕ b<∞) and is embedded in d-dimensional Euclidean space. In the two-dimensional (2D) and three-dimensional (3D) case, we find expressions for the residual entropy σ( b) for arbitrary b, and show that in the limit b→∞ the calculated values should converge to the values pertinent to the corresponding Euclidean lattices. In particular, these results confirm recent findings concerning the residual entropy of the 2D Sierpinski gasket type of fractals, obtained by numerical fitting. We also study the d-dimensional case and find a general expression for σ( b) for arbitrary b⪖3.