Annales de l’Institut Henri Poincaré D


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Volume 5, Issue 2, 2018, pp. 251–286
DOI: 10.4171/AIHPD/54

Published online: 2018-06-04

A symmetry breaking transition in the edge/triangle network model

Charles Radin[1], Kui Ren[2] and Lorenzo Sadun[3]

(1) University of Texas, Austin, USA
(2) University of Texas, Austin, USA
(3) University of Texas, Austin, USA

Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp transition between two phases with different symmetries, analogous to the transition between a fluid and a crystalline solid.

Keywords: Graph limits, entropy, bipodal structure, phase transitions, symmetry breaking

Radin Charles, Ren Kui, Sadun Lorenzo: A symmetry breaking transition in the edge/triangle network model. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 5 (2018), 251-286. doi: 10.4171/AIHPD/54