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On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field

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arxiv 2103.04802 v2 pith:H5N73ENU submitted 2021-03-08 cond-mat.dis-nn math-phmath.MPmath.PR

On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field

classification cond-mat.dis-nn math-phmath.MPmath.PR
keywords transitionalmeida-thoulesscenteredexternalfieldgaussianlinemodel
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We study the phase transition of the free energy in the Sherrington-Kirkpatrick mean-field spin glass model with centered Gaussian external field. We show that the corresponding Almeida-Thouless line is the correct transition curve that distinguishes between the replica symmetric and replica symmetry breaking solutions in the Parisi formula.

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    Proves self-averaging of replica overlaps in the random-field EA model in any dimension using free energy derivatives and Tasaki's inequality.