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

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

2010-04-21

arxiv.org/abs/1004.3622v3

Phys. Rev. E 82, 060103(R) (2010)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 5 figures; clarifications and discussion about boundary effects is added

Scientific paper

10.1103/PhysRevE.82.060103

Relationships between general long-range interacting classical systems on a lattice and the corresponding mean-field models (infinitely long-range interacting models) are investigated. We study systems in arbitrary dimension d for periodic boundary conditions and focus on the free energy for fixed value of the total magnetization. As a result, it is shown that the equilibrium free energy of the long-range interacting systems are exactly the same as that of the corresponding mean-field models (exactness of the mean-field theory). Moreover, the mean-field metastable states can be also preserved in general long-range interacting systems. It is found that in the case that the magnetization is conserved, the mean-field theory does not give correct property in some parameter region.

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