The high temperature region of the Viana-Bray diluted spin glass model

Abstract

In this paper, we study the high temperature or low connectivity phase of the Viana-Bray model. This is a diluted version of the well known Sherrington-Kirkpatrick mean field spin glass. In the whole replica symmetric region, we obtain a complete control of the system, proving annealing for the infinite volume free energy, and a central limit theorem for the suitably rescaled fluctuations of the multi-overlaps. Moreover, we show that free energy fluctuations, on the scale 1/N, converge in the infinite volume limit to a non-Gaussian random variable, whose variance diverges at the boundary of the replica-symmetric region. The connection with the fully connected Sherrington-Kirkpatrick model is discussed.

24 pages

References in corpus (1)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

Cited by in corpus (12)

• The mean field Ising model trough interpolating techniques
• Cavity analysis on the robustness of random networks against targeted attacks: Influences of degree-degree correlations
• Mean field dilute ferromagnet I. High temperature and zero temperature behavior
• Strong replica symmetry for high-dimensional disordered log-concave Gibbs measures
• Analogue neural networks on correlated random graphs
• Graph's Topology and Free Energy of a Spin Model on the Graph
• Some Observations for Mean-Field Spin Glass Models
• Dilution Robustness for Mean Field Ferromagnets
• Free energy of a diluted spin glass model with quadratic Hamiltonian
• Mean Field Spin Glass Models under Weak External Field
• Replica bound for Ising spin glass models in one dimension
• Free energy equivalence between mean-field models and nonsparsely diluted mean-field models