Free energy of magnetic model systems at the fractal to Euclidian crossover

Abstract

We prove that the free energy per spin of the nearest-neighbour classical n-vector spin model situated on the Sierpinski gasket (SG) family of fractals tends to the free energy per spin of the same model situated on the standard triangular lattice, when the linear size b of the SG fractal generator tends to infinity. This finding can be regarded as the first step in the analytical investigation of the spin system thermodynamics at the fractal to Euclidean crossover. © 1990.