1111.1046 (Takashi Mori)

Microcanonical Analysis of Exactness of the Mean-Field Theory in
Long-Range Interacting Systems    [PDF]

Takashi Mori

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 \alpha-Potts model with annealed vacancies and the \alpha-Potts model with invisible states.

View original: http://arxiv.org/abs/1111.1046