Analytical verification of scaling laws for the Ising model with external field in fractal lattices

Abstract

We use an exact recursion procedure to verify analytically, without any intermediary numerical calculation, the validity of the hyperscaling (Josephson) law extended to fractals, the Rushbrooke and Griffiths scaling laws for the Ising ferromagnet with external magnetic field in the whole family of Migdal-Kadanoff-like hierarchical lattices.