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 Nb w black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in the emergence of a wide plateau on the Nb w(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.
- Publication:
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Physical Review E
- Pub Date:
- January 2016
- DOI:
- 10.1103/PhysRevE.93.012302
- arXiv:
- arXiv:1506.00205
- Bibcode:
- 2016PhRvE..93a2302A
- Keywords:
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- Condensed Matter - Statistical Mechanics;
- High Energy Physics - Phenomenology;
- High Energy Physics - Theory
- E-Print:
- 9 pages, 4 figures