Toward mean-field bound for critical temperature on Nishimori line

• Main Authors: Okuyama, Manaka, Ohzeki, Masayuki
• Format: Journal Article
• Language: English
• Published: 24-09-2024
• Subjects: Physics - Disordered Systems and Neural Networks; Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.2406.12728

J. Phys. Soc. Jpn. 93, 104706 (2024) 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
$\beta_{MF}^{NL}=\sqrt{1/z}$, 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 $\beta <
\beta_{MF}^{NL}/2$. In other words, the true critical inverse temperature
$\beta_c^{NL}$ on the Nishimori line is always bounded by $\beta_c^{NL} \ge
\beta_{MF}^{NL}/2$. Unfortunately, we have not succeeded in obtaining the
corresponding mean-field bound $\beta_c^{NL} \ge \beta_{MF}^{NL}$ on the
Nishimori line.