title: Spontaneous symmetry breaking and phase coexistence in two-color networks.
abstract: We consider an equilibrium ensemble of large Erdős-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 N_{bw} black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in the emergence of a wide plateau on the N_{bw}(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.
authors: N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia.|Department of Applied Mathematics, National Research University Higher School of Economics, Moscow 101000, Russia.
authors: V
authors: V
authors: Avetisov
authors: Institute of Information Transmission Problems, Russian Academy of Sciences, Moscow 127051, Russia.|Moscow Institute of Physics and Technology, Dolgoprudny 141700, Russia.
authors: A
authors: A
authors: Gorsky
authors: Université Paris-Sud, CNRS, LPTMS, UMR No. 8626, Bâtiment 100, 91405 Orsay, France.|P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991, Russia.
authors: S
authors: S
authors: Nechaev
authors: N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow 119991, Russia.|Department of Applied Mathematics, National Research University Higher School of Economics, Moscow 101000, Russia.
authors: O
authors: O
authors: Valba