High-temperature expansions on Sierpinski carpets

Abstract

A method that allows one to compute the lattice constants of graphs embedded on regular fractal lattices is given. As an application, considering the Ising model on various Sierpinski carpets, we derive the high-temperature expansion up to the ninth order of the magnetic susceptibility. In order to complete and sharpen previous estimates, we give the values of the critical temperature and exponent \ensuremath{\gamma} derived from their Pad\'e approximants.