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 non-equilibrium 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. 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.