Transfer matrix studies of branching fractals

Abstract

We introduce the method of transfer matrices to study physical models defined on branching fractal lattices. In this context we derive matricial recurrence relations, connecting the matrices associated with successive fractal generations. These relations depend only on the geometry of the fractal and may be used for any model. Explicit results are obtained for ferromagnetic and antiferromagnetic Ising models on branching Koch curves and Sierpiński gasket.