Ising spin glass models versus Ising models: an effective mapping at high temperature I. General result

Abstract

We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense, D is infinite, in the paramagnetic phase and on its boundary the mapping is exact. In this limit the method provides a general and simple rule to obtain exactly the upper phase boundaries. We provide even simple effective rules to find crossover surfaces and correlation functions. We apply the mapping to several spin glass models.

38 pages, 12 Postscript figures

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• Critical behavior and correlations on scale-free small-world networks. Application to network design
• Ising spin glass models versus Ising models: an effective mapping at high temperature II. Applications to graphs and networks
• Ising spin glass models versus Ising models: an effective mapping at high temperature III. Rigorous formulation and detailed proof for general graphs
• Absence of small-world effects at the quantum level and stability of the quantum critical point