Replica theory for Levy spin glasses

Abstract

Infinite-range spin-glass models with Levy-distributed interactions show a spin-glass transition with similarities to both the Sherrington-Kirkpatrick model and to disordered spin systems on finite connectivity random graphs. Despite the diverging moments of the coupling distribution the transition can be analyzed within the replica approach by working at imaginary temperature. Within the replica-symmetric approximation a self-consistent equation for the distribution of local fields is derived and from the instability of the paramagnetic solution to this equation the glass-transition temperature is determined. The role of the percolation of rare strong bonds for the transition is elucidated. The results partly agree and partly disagree with those obtained within the cavity approach. Numerical simulations using parallel tempering are in agreement with the transition temperatures found.

12 pages, 2 figures, to appear in JSTAT

References in corpus (8)

• Statistical mechanics of complex networks
• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• The Bethe lattice spin glass revisited
• Monte Carlo Simulations of Spin Glasses at Low Temperatures
• Optimisation problems and replica symmetry breaking in finite connectivity spin-glasses
• Public channel cryptography by synchronization of neural networks and chaotic maps
• Matrix Games, Mixed Strategies, and Statistical Mechanics
• Random quantum magnets with broad disorder distribution

Cited by in corpus (12)

• Existence of a Thermodynamic Spin-Glass Phase in the Zero-Concentration Limit of Anisotropic Dipolar Systems
• The phase diagram of Lévy spin glasses
• Thermodynamics of the Lévy spin glass
• The Levy spin glass transition
• Critical behavior and universality in Levy spin glasses
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
• Reduction of Dilute Ising Spin Glasses
• Ground States of the Sherrington-Kirkpatrick Spin Glass with Levy Bonds
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Stability of the replica-symmetric saddle-point in general mean-field spin-glass models
• The dipolar spin glass transition in three dimensions
• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with heavy-tailed interaction