Ising model from intertwiners

Abstract

Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show how a certain generating function of intertwiner contractions for arbitrary networks, when restricted to a square lattice is exactly related to the high temperature expansion of the 2d Ising model partition function. This implies that the intertwiner model possesses a second order phase transition, thus leading to a continuum limit with propagating degrees of freedom.