Analysis of the exactness of mean-field theory in long-range interacting systems.
Analysis of the exactness of mean-field theory in long-range interacting systems.
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远程相互作用系统中平均场理论的准确性分析。
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发表时间：
2010
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通讯作者：
Takashi Mori
中科院分区：
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作者：
Takashi Mori
研究了一般长程相互作用经典系统与相应的平均场模型（无限长程相互作用模型）之间的关系。我们研究系统在任意维d周期性边界条件和集中的自由能固定值的总磁化。结果表明，长程相互作用系统的平衡自由能与相应的平均场模型的平衡自由能完全相同（平均场理论的正确性）。此外，在一般的长程相互作用系统中，平均场亚稳态也能保持。结果表明，在磁化强度守恒的情况下，平均场理论在某些参数区域不能给出正确的性质。
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.