Toward mean-field bound for critical temperature on Nishimori line

Abstract

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.

10pages, 0 figure

References in corpus (9)

• Locations of multicritical points for spin glasses on regular lattices
• Gauge Theory for Quantum Spin Glasses
• Continuous symmetry breaking along the Nishimori line
• Non-equilibrium Relations for Spin Glasses with Gauge Symmetry
• Gibbs-Bogoliubov inequality on Nishimori line
• Analyticity of the energy in an Ising spin glass with correlated disorder
• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models
• Mean-field theory is exact for Ising spin glass models with Kac potential in non-additive limit on Nishimori line
• Gauge theory for mixed $p$-spin glasses