Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems.

Classical spin systems with nonadditive long-range interactions are studied in the microcanonical ensemble. It is expected that the entropy of such a system is identical to that of the corresponding mean-field model, which is called 'exactness of the mean-field theory'. It is found out that this expectation is not necessarily true if the microcanonical ensemble is not equivalent to the canonical ensemble in the mean-field model. Moreover, necessary and sufficient conditions for exactness of the mean-field theory are obtained. These conditions are investigated for two concrete models, the α-Potts model with annealed vacancies and the α-Potts model with invisible states. [ABSTRACT FROM AUTHOR]