Toward mean-field bound for critical temperature on Nishimori line
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914955553406976 |
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| author | Okuyama, Manaka Ohzeki, Masayuki |
| author_facet | Okuyama, Manaka Ohzeki, Masayuki |
| contents | The critical inverse temperature of the mean-field approximation establishes a lower bound of the true critical inverse temperature in a broad class of ferromagnetic spin models. This is referred to as the mean-field bound for the critical temperature. In this study, we explored the possibility of a corresponding mean-field bound for the critical temperature in Ising spin glass models with Gaussian randomness on the Nishimori line. On this line, the critical inverse temperature of the mean-field approximation is given by $β_{MF}^{NL}=\sqrt{1/z}$, where $z$ is the coordination number. Using the Griffiths inequalities on the Nishimori line, we proved that there is zero spontaneous magnetization in the high-temperature region $β< β_{MF}^{NL}/2$. In other words, the true critical inverse temperature $β_c^{NL}$ on the Nishimori line is always bounded by $β_c^{NL} \ge β_{MF}^{NL}/2$. Unfortunately, we have not succeeded in obtaining the corresponding mean-field bound $β_c^{NL} \ge β_{MF}^{NL}$ on the Nishimori line. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_12728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toward mean-field bound for critical temperature on Nishimori line Okuyama, Manaka Ohzeki, Masayuki Disordered Systems and Neural Networks Statistical Mechanics The critical inverse temperature of the mean-field approximation establishes a lower bound of the true critical inverse temperature in a broad class of ferromagnetic spin models. This is referred to as the mean-field bound for the critical temperature. In this study, we explored the possibility of a corresponding mean-field bound for the critical temperature in Ising spin glass models with Gaussian randomness on the Nishimori line. On this line, the critical inverse temperature of the mean-field approximation is given by $β_{MF}^{NL}=\sqrt{1/z}$, where $z$ is the coordination number. Using the Griffiths inequalities on the Nishimori line, we proved that there is zero spontaneous magnetization in the high-temperature region $β< β_{MF}^{NL}/2$. In other words, the true critical inverse temperature $β_c^{NL}$ on the Nishimori line is always bounded by $β_c^{NL} \ge β_{MF}^{NL}/2$. Unfortunately, we have not succeeded in obtaining the corresponding mean-field bound $β_c^{NL} \ge β_{MF}^{NL}$ on the Nishimori line. |
| title | Toward mean-field bound for critical temperature on Nishimori line |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2406.12728 |