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Статья

Spontaneous symmetry breaking and phase coexistence in two-color networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2016. Vol. 93. No. 1. P. 012302-1-012302-7.
Avetisov V. A., Gorsky A., Nechaev S., Valba O. V.

We consider an equilibrium ensemble of large Erdos-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 μ. Minimizing the system energy, we see for some positive μ the formation of two predominantly unicolor clusters, linked by a string of Nbw black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in the emergence of a wide plateau on the Nbw(μ) curve, which is relevant to a spinodal decomposition in first-order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby universes in two-dimensional gravity. We conjecture that the observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.