The phases of large networks with edge and triangle constraints. (4th October 2017)

• Record Type: Journal Article
• Authors: Kenyon, Richard; Radin, Charles; Ren, Kui; Sadun, Lorenzo
• Is Part Of: Journal of physics. Volume 50:Number 43(2017)
• Publication Date: 2017-10-04
• Subjects: random graphs -- phase diagram -- phase transitions; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa8ce1
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for many of the phase transitions. All but one of the many phase transitions in this model break some form of symmetry, and we use this model to explore how changes in symmetry are related to discontinuities at these transitions.