Disorder chaos in the spherical mean-field model

Abstract

We consider the problem of disorder chaos in the spherical mean-field model. It is concerned about the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters. The prediction states that if the disorders in the Hamiltonians are slightly decoupled, then the overlap will be concentrated near a constant value. Following Guerra's replica symmetry breaking scheme, we establish this at the level of the free energy as well as the Gibbs measure irrespective the presence or absence of the external field.

arXiv comment12 pages

References in corpus (4)

• On the overlap in the multiple spherical SK models
• Disorder chaos and multiple valleys in spin glasses
• Disorder chaos in the Sherrington-Kirkpatrick model with external field
• Chaos in temperature in generic 2p-spin models

Cited by in corpus (10)

• The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra
• Parisi formula, disorder chaos and fluctuation for the ground state energy in the spherical mixed p-spin models
• Spectral gap estimates in mean field spin glasses
• Topology trivialization transition in random non-gradient autonomous ODE's on a sphere
• On the energy landscape of the mixed even $p$-spin model
• The Crisanti-Sommers Formula for Spherical Spin Glasses with Vector Spins
• Sampling from Mean-Field Gibbs Measures via Diffusion Processes
• On properties of the spherical mixed vector p-spin model
• Free Energy Subadditivity for Symmetric Random Hamiltonians
• On Marginal Stability in Low Temperature Spherical Spin Glasses