We provide a rigorous strategy to find the critical exponents of the overlaps for dilute spin glasses, in the absence of an external field. Such a strategy is based on the expansion of a suitably perturbed average of the overlaps, which is used in the formulation of the free energy as the difference between a cavity part and the derivative of the free energy itself, considered as a function of the connectivity of the model. We assume the validity of certain reasonable approximations, equivalent to assuming a second-order transition, e. g. that higher powers of overlap monomials are of smaller magnitude near the critical point, of which we do not provide a rigorous proof.

Critical behavior of mean-field spin glasses on a dilute random graph / Luca De, Sanctis; Barra, Adriano; Folli, Viola. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 41:21(2008), p. 215005. [10.1088/1751-8113/41/21/215005]

Critical behavior of mean-field spin glasses on a dilute random graph

BARRA, ADRIANO;
2008

Abstract

We provide a rigorous strategy to find the critical exponents of the overlaps for dilute spin glasses, in the absence of an external field. Such a strategy is based on the expansion of a suitably perturbed average of the overlaps, which is used in the formulation of the free energy as the difference between a cavity part and the derivative of the free energy itself, considered as a function of the connectivity of the model. We assume the validity of certain reasonable approximations, equivalent to assuming a second-order transition, e. g. that higher powers of overlap monomials are of smaller magnitude near the critical point, of which we do not provide a rigorous proof.
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Critical behavior of mean-field spin glasses on a dilute random graph / Luca De, Sanctis; Barra, Adriano; Folli, Viola. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 41:21(2008), p. 215005. [10.1088/1751-8113/41/21/215005]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/442855
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