平均场模型与非稀疏稀释平均场模型之间的自由能等价性
Free energy equivalence between mean-field models and nonsparsely diluted mean-field models
AI总结：
本研究严格证明了在热力学极限下，具有伯努利边分布的非稀疏稀释平均场模型，其自由能与相应平均场模型精确等价，推广了先前关于稀释Curie--Weiss模型的结果。
摘要：
我们研究了与非稀疏稀释平均场模型不同的非稀疏稀释平均场模型，例如Viana--Bray模型。当每条边的存在概率服从伯努利分布时，我们严格证明了在热力学极限下，具有适当参数化的非稀疏稀释平均场模型，对于由任意离散自旋$S$组成的铁磁和自旋玻璃模型，其自由能与相应平均场模型的自由能完全一致。我们的结果是对先前研究[Bovier和Gayrard，J. Stat. Phys. 72, 643 (1993)]结果的广泛推广，该研究严格分析了具有适当参数化的稠密稀释平均场铁磁Ising模型（稀释Curie--Weiss模型），并证明了其自由能与相应平均场模型（Curie--Weiss模型）的自由能精确等价。
英文摘要：
We studied nonsparsely diluted mean-field models that differ from sparsely diluted mean-field models, such as the Viana--Bray model. When the existence probability of each edge follows a Bernoulli distribution, we rigorously prove that the free energy of nonsparsely diluted mean-field models with appropriate parameterization coincides exactly with that of the corresponding mean-field models in ferromagnetic and spin-glass models composed of any discrete spin $S$ in the thermodynamic limit. Our results is a broad generalization of the result of a previous study [Bovier and Gayrard, J. Stat. Phys. 72, 643 (1993)], where the densely diluted mean-field ferromagnetic Ising model (diluted Curie--Weiss model) with appropriate parameterization was analyzed rigorously, and it was proven that its free energy was exactly equivalent to that of the corresponding mean-field model (Curie--Weiss model).
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