A symmetry breaking transition in the edge/triangle network model. (English) Zbl 1390.05218
Summary: 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.
MSC:
05C80 | Random graphs (graph-theoretic aspects) |
05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
82B26 | Phase transitions (general) in equilibrium statistical mechanics |