The phase diagram of Lévy spin glasses

Abstract

We study the Lévy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of Lévy spin glasses becomes transparent in our solution: the local field contains a part propagating along a backbone of strong bonds and a Gaussian noise term due to weak bonds. Our method allows to determine the complete replica symmetric phase diagram, the replica symmetry breaking line and the entropy. The results are compared with simulations and previous calculations using a Gaussian ansatz for the distribution of fields.

20 pages, 7 figures

References in corpus (5)

• Extreme value problems in Random Matrix Theory and other disordered systems
• Gallager error correcting codes for binary asymmetric channels
• Replica theory for Levy spin glasses
• Equilibrium properties of disordered spin models with two scale interactions
• On composite systems of dilute and dense couplings

Cited by in corpus (18)

• On the localization transition in symmetric random matrices
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• The Spectral Backbone of Excitation Transport in Ultra-Cold Rydberg Gases
• Impact of correlations and heavy-tails on quantum error correction
• Thermodynamics of the Lévy spin glass
• Localization transition in random Levy matrices : multifractality of eigenvectors in the localized phase and at criticality
• The Levy spin glass transition
• Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World
• Critical behavior and universality in Levy spin glasses
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
• Ising spin glass in a random network with a gaussian random field
• 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
• Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics
• Generalized Lotka-Volterra model with sparse interactions: non-Gaussian effects and topological multiple-equilibria phase
• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with heavy-tailed interaction
• Mean-field theory of vector spin models on networks with arbitrary degree distributions