Ising model from intertwiners
Annales de l’Institut Henri Poincaré D, Tome 3 (2016) no. 4, pp. 363-380.

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.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/32
Classification : 82-XX, 83-XX
Mots-clés : Ising model, spin networks, loop quantum gravity 
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     title = {Ising model from intertwiners},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {363--380},
     volume = {3},
     number = {4},
     year = {2016},
     doi = {10.4171/aihpd/32},
     zbl = {1375.82071},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/32/}
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Dittrich, Bianca; Hnybida, Jeff. Ising model from intertwiners. Annales de l’Institut Henri Poincaré D, Tome 3 (2016) no. 4, pp. 363-380. doi : 10.4171/aihpd/32. http://archive.numdam.org/articles/10.4171/aihpd/32/

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