Griffiths inequalities for the Gaussian spin glass

Details Griffiths inequalities for the Gaussian spin glass Griffiths inequalities for the Gaussian spin glass

2004-03-25

arxiv.org/abs/cond-mat/0403625v2

J. Phys. A 37 (2004) L203

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages; Added references

Scientific paper

10.1088/0305-4470/37/18/L03

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.

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