Thermal properties of structurally balanced systems on classical random graphs

The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) under the influence of the temperature modeling the social noise level are discussed for interacting actors occupying nodes of classical random graphs. Depending on the graph density D, either a smooth crossover or a first-order phase transition from a balanced to an imbalanced state of the system is observed with an increase in the thermal noise level. The minimal graph density Dmin for which the first-order phase transition can be observed decreases with the system size N as Dmin∝N-0.58(1). For graph densities D>Dmin, the reduced critical temperature Tc⋆=Tc/Tc(D=1) increases with the graph density as Tc⋆∝D1.719(6) independently of the system size N.