Griffiths inequalities and Gibbs-Bogoliubov inequality for general gauge glasses with Gaussian disorder on Nishimori line
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866908999001047040 |
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| author | Okuyama, Manaka Ohzeki, Masayuki |
| author_facet | Okuyama, Manaka Ohzeki, Masayuki |
| contents | We consider a class of gauge glass models with Gaussian disorder on the Nishimori line, including the Ising spin glass, the $XY$ gauge glass, the $Z_q$ gauge glass, and the gauge-invariant Potts model. We prove that the first and second Griffiths inequalities hold for these models on arbitrary lattice structures. As a consequence, both the pressure and the correlation functions are monotonically increasing with respect to the inverse temperature along the Nishimori line. Furthermore, we establish an analogue of the Gibbs--Bogoliubov inequality for this class of models. This result implies that, on the Nishimori line, the approximate quenched free energy obtained via the replica method with a replica-symmetric mean-field approximation is always greater than the true quenched free energy. Our results provide a broad generalization of previous results established for the Ising spin glass with Gaussian disorder on the Nishimori line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25697 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Griffiths inequalities and Gibbs-Bogoliubov inequality for general gauge glasses with Gaussian disorder on Nishimori line Okuyama, Manaka Ohzeki, Masayuki Mathematical Physics Disordered Systems and Neural Networks Statistical Mechanics Probability We consider a class of gauge glass models with Gaussian disorder on the Nishimori line, including the Ising spin glass, the $XY$ gauge glass, the $Z_q$ gauge glass, and the gauge-invariant Potts model. We prove that the first and second Griffiths inequalities hold for these models on arbitrary lattice structures. As a consequence, both the pressure and the correlation functions are monotonically increasing with respect to the inverse temperature along the Nishimori line. Furthermore, we establish an analogue of the Gibbs--Bogoliubov inequality for this class of models. This result implies that, on the Nishimori line, the approximate quenched free energy obtained via the replica method with a replica-symmetric mean-field approximation is always greater than the true quenched free energy. Our results provide a broad generalization of previous results established for the Ising spin glass with Gaussian disorder on the Nishimori line. |
| title | Griffiths inequalities and Gibbs-Bogoliubov inequality for general gauge glasses with Gaussian disorder on Nishimori line |
| topic | Mathematical Physics Disordered Systems and Neural Networks Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2604.25697 |