Residual entropies of the Ising antiferromagnets on fractals: II. d-dimensional checkerboard type of fractals

Abstract

We study the residual entropies of the antiferromagnetic Ising systems, in the maximum critical field, situated on checkerboard (CB) type of fractals embedded in d-dimensional Euclidean space. For a given d, the CB fractals constitute a family, whose each member is labelled by b, where b is an odd integer (3⪕ b<∞). Each family itself furnishes a crossover to the corresponding d-dimensional hypercubic lattice. By calculating explicitly residual entropies σ( b) for finite b, and by using a specific method of extrapolating the obtained results, we were able to establish the crossover behavior of σ( b). It turns out that the established crossover is of the same type as the one found in the case of fractal families of the Sierpinski gasket type.