Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass

Abstract

Sample-to-sample free energy fluctuations in spin-glasses display a markedly different behaviour in finite-dimensional and fully-connected models, namely Gaussian vs. non-Gaussian. Spin-glass models defined on various types of random graphs are in an intermediate situation between these two classes of models and we investigate whether the nature of their free-energy fluctuations is Gaussian or not. It has been argued that Gaussian behaviour is present whenever the interactions are locally non-homogeneous, i.e. in most cases with the notable exception of models with fixed connectivity and random couplings $J_{ij}=\pm \tilde{J}$. We confirm these expectation by means of various analytical results. In particular we unveil the connection between the spatial fluctuations of the populations of populations of fields defined at different sites of the lattice and the Gaussian nature of the free-energy fluctuations. On the contrary on locally homogeneous lattices the populations do not fluctuate over the sites and as a consequence the small-deviations of the free energy are non-Gaussian and scales as in the Sherrington-Kirkpatrick model.

References in corpus (3)

• Finite size corrections in the Sherrington-Kirkpatrick model
• Universality-class dependence of energy distributions in spin glasses
• The Ising spin glass in finite dimensions: a perturbative study of the free energy

Cited by in corpus (12)

• One-dimensional infinite component vector spin glass with long-range interactions
• The marginally stable Bethe lattice spin glass revisited
• Chaos in Temperature in Diluted Mean-Field Spin-Glasses
• Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass
• Finite size scaling of the de Almeida-Thouless instability in random sparse networks
• A singular-potential random matrix model arising in mean-field glassy systems
• Numerical Results for Spin Glass Ground States on Bethe Lattices: Gaussian Bonds
• Ground States of the Sherrington-Kirkpatrick Spin Glass with Levy Bonds
• Adversarial Satisfiability Problem
• Large deviations of the free energy in the p-spin glass spherical model
• Sample-to-sample fluctuations and bond chaos in the $m$-component spin glass
• Temperature chaos and quenched heterogeneities