A symmetry breaking transition in the edge/triangle network model

TL;DR

This paper analyzes a phase transition in a network model constrained by edge and triangle densities, revealing a symmetry-breaking transition similar to physical phase changes.

Contribution

It introduces a detailed analysis of a symmetry-breaking phase transition in a network model constrained by edge and triangle subdensities.

Findings

Identification of a sharp transition between two symmetry-different phases

Analogous behavior to fluid and crystalline solid transition

Characterization of phase boundaries in the edge/triangle network model

Abstract

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.