Stability and ensemble inequivalence in a globally coupled system
Abstract
We consider a system of globally coupled rotors, described by a set of Langevin equations, and examine stability of the incoherent phase. The corresponding Fokker-Planck equation, providing a unified description of microcanonical and canonical ensembles, bears a few solutions, depending upon the ensemble. It is found that the stability of each solution varies differently with the temperature, revealing the inequivalence between the two ensembles. This also suggests a physical explanation of the quasi-stationarity observed in recent numerical results.
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