Free energy equivalence between mean-field models and nonsparsely diluted mean-field models

Manaka Okuyama; Masayuki Ohzeki

doi:10.1088/1751-8121/adaab4

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arXiv · 2406.13245

Free energy equivalence between mean-field models and nonsparsely diluted mean-field models

Manaka Okuyama·Masayuki Ohzeki

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Abstract

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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Manaka Okuyama, Masayuki Ohzeki. 2024-06-19. Free energy equivalence between mean-field models and nonsparsely diluted mean-field models. https://doi.org/10.1088/1751-8121/adaab4

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