Phase Transitions in Equilibrium and Non-Equilibrium Models on Some Topologies

Exact solution of the isotropic majority-vote model on complete graphs

The isotropic majority-vote (MV) model, which, apart from the one-dimensional case, is thought to be nonequilibrium and violating the detailed balance condition. We show that this is not true when the model is defined on a complete graph. In the stationary regime, the MV model on a fully connected graph fulfills the detailed balance and is equivalent to the modified Ehrenfest urn model. Using the master equation approach, we derive the exact expression for the probability distribution of finding the system in a given spin configuration. We show that it only depends on the absolute value of magnetization. Our theoretical predictions are validated by numerical simulations.