Griffiths inequalities for the Gaussian spin glass

TL;DR

This paper proves Griffiths inequalities for Gaussian spin glasses, showing non-negative correlations and monotonicity, and establishes the existence of thermodynamic limits and relations between multicritical points.

Contribution

It introduces new inequalities for Gaussian spin glasses, extending understanding of correlation behaviors and phase diagram properties in these models.

Findings

Correlation functions are non-negative and monotonic along the Nishimori line.

Thermodynamic limits for correlation functions and pressure are established.

Relations between multicritical points on different lattices are derived.

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.