Griffiths inequalities for the Gaussian spin glass

Abstract

The Griffiths inequalities for Ising spin-glass models with Gaussian randomness of non-vanishing mean are proved using properties of the Gaussian distribution and gauge symmetry of the system. These inequalities imply that correlation functions are non-negative and monotonic along the Nishimori line in the phase diagram. From this result, the existence of thermodynamic limit for correlation functions and pressure is proved under free and fixed boundary conditions. Relations between the location of multicritical points are also derived for different lattices.

8 pages; Added references

References in corpus (3)

• The Thermodynamic Limit in Mean Field Spin Glass Models
• Thermodynamical Limit for Correlated Gaussian Random Energy Models
• Monotonicity and Thermodynamic Limit for Short Range Disordered Models

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• Free-energy bounds for hierarchical spin models
• Gibbs-Bogoliubov inequality on Nishimori line
• Inequalities for the Local Energy of Random Ising Models
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• Boundedness of Susceptibility in Spin Glass Transition of Transverse Field Mixed $p$-spin Glass Models
• Gauge theory for mixed $p$-spin glasses
• Inequality for local energy of Ising models with quenched randomness and its application
• Toward mean-field bound for critical temperature on Nishimori line
• Applications of correlation inequalities to low density graphical codes
• Gauge theory for quantum XYZ spin glasses