A symmetry breaking transition in the edge/triangle network model
  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. 
Charles Radin and Kui Ren and Lorenzo Sadun
math.CO cond-mat.stat-mech cs.SI math.PR