Annales de l’Institut Henri Poincaré D

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Volume 3, Issue 4, 2016, pp. 363–380
DOI: 10.4171/AIHPD/32

Published online: 2016-12-22

Ising model from intertwiners

Bianca Dittrich[1] and Jeff Hnybida[2]

(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