Phase Transitions for Mean Field Processes

#### V.M. Gertsik, E.N. Petrova, S.A. Pirogov

2017, v.23, №4, 679-687

ABSTRACT

We study the distribution of an average spin for a mean field jump
process in a multiphase regime. We show that in this case a limit distribution of an average spin is concentrated on several points. For example, we prove the existence
of a phase transition for the stationary states of noise-induced barrier
hopping processes. In this model there is a line of phase transitions on the parameter plane. This line starts in the critical point.

Keywords: phase transition, multicomponent random processes, mean field, stationary distribution, law of large numbers, critical point