# Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks

### V. Avetisov 1, 2 A. Gorsky 3, 4 S. Nechaev 5, 6 O. Valba 1, 2

#### Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2016, 93, pp.012302

We have considered an equilibrium ensemble of large Erd\H{o}s-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly with the bond connection probability, $p$. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples, $\mu$. Minimizing the system energy, we see for some positive $\mu$ formation of two predominantly unicolor clusters, linked by a "string" of $N_{bw}$ black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in emergence of a wide plateau on the $N_{bw}(\mu)$-curve, which is relevant to a spinodal decomposition in 1st order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby-universes in 2D gravity. We have conjectured that observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.

• 1. The Semenov Institute of Chemical Physics
• 2. Department of Applied Mathematics
• 3. IITP - Institute for Information Transmission Problems
• 4. MIPT - Moscow Institute of Physics and Technology [Moscow]
• 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 6. P. N. Lebedev Physical Institute [Moscow]