Potts model on the Sierpinski gasket: A transfer-matrix approach

Abstract

The q-states Potts model on the Sierpj. nski gasket with ferromagnetic and antiferromagnetic interactions is analyzed with use of the transfer-matrix method. It leads to a set of four coupled maps for the free energy and correlation length. Attention is focused on the behavior of the residual entropy, when 1, 2, or 3 bonds within a unit cell is antiferromagnetic. In the isotropic case, with q=4, the value for so is larger than that of the triangular lattice. The isotropic ferromagnetic model shows an unusual sharp peak in the specific heat in the limit of large q.