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

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

2006-07-19

arxiv.org/abs/cond-mat/0607498v1

J. Stat. Mech. (2006) P10004

Physics

Condensed Matter

Statistical Mechanics

38 pages, 12 Postscript figures

Scientific paper

10.1088/1742-5468/2006/10/P10004

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.

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