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

griffiths inequalities in the nishimori line

CONTUCCI, PIERLUIGI;
2004

Abstract

The Griffiths inequalities for Ising spin-glass models with Gaussian randomness of non-vanishing mean are proved using the properties of the Gaussian distribution and the gauge symmetry of the system. These inequalities imply that the correlation functions are non-negative and monotonic along the Nishimori line in the phase diagram. From this result, the existence of the thermodynamic limit for the correlation functions and the free energy is proved under free and fixed boundary conditions. Relations between the location of multi-critical points are also derived for different lattices.
Pierluigi Contucci; Satoshi Morita; Hidetoshi Nishimori
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/4950
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