Central limit theorem near the critical temperature for the overlap in the 2-spin spherical SK model

Abstract

We prove a central limit theorem for the normalized overlap between two replicas in the spherical SK model in the high temperature phase. The convergence holds almost surely with respect to the disorder variables, and the inverse temperature can approach the criticial value at a polynomial rate with any exponent strictly greater than $1/3$.

arXiv comment16 pages

References in corpus (8)

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• Lectures on the local semicircle law for Wigner matrices
• On the overlap in the multiple spherical SK models
• Topology trivialization and large deviations for the minimum in the simplest random optimization
• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model
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Cited by in corpus (6)

• Spherical spin glass model with external field
• Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model
• Free energy fluctuations of the $2$-spin spherical SK model at critical temperature
• Mean Field Spin Glass Models under Weak External Field
• Overlap of a spherical spin glass model with microscopic external field
• Generalised Gibbs Ensemble for spherically constrained harmonic models