Annales de l’Institut Henri Poincaré D
Full-Text PDF (272 KB) | Metadata | Table of Contents | AIHPD summary
Published online: 2016-12-22
Ising model from intertwinersBianca Dittrich and Jeff Hnybida (1) Perimeter Institute for Theoretical Physics, Waterloo, Canada
(2) Perimeter Institute for Theoretical Physics, Waterloo, Canada
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.
Keywords: Ising model, spin networks, loop quantum gravity
Dittrich Bianca, Hnybida Jeff: Ising model from intertwiners. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 3 (2016), 363-380. doi: 10.4171/AIHPD/32