The role of the interaction matrix in mean-field spin glasses

Abstract

Mean-field models of 2-spin Ising spin glasses with interaction matrices taken from ensembles which are invariant under O(N) transformations are studied. A general study shows that the nature of the spin glass transition can be deduced from the eigenvalue spectrum of the interaction matrix. A simple replica approach is derived to carry out the average over the O(N) disorder. The analytic results are confirmed by extensive Monte Carlo simulations for large system sizes and by exact enumeration for small system sizes.

14 pages, 4 figures

Cited by in corpus (23)

• On the critical slowing down exponents of mode coupling theory
• Metastable states and space-time phase transitions in a spin-glass model
• Why glass elasticity affects the thermodynamics and fragility of super-cooled liquids
• Inference from correlated patterns: a unified theory for perceptron learning and linear vector channels
• High-temperature Expansions and Message Passing Algorithms
• Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
• Perceptron capacity revisited: classification ability for correlated patterns
• Mechanisms of dimensionality reduction and decorrelation in deep neural networks
• Inverse Freezing in Mean-Field Models of Fragile Glasses
• Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
• Equilibrium Fluctuations in Mean-field Disordered Models
• Adaptive Thouless-Anderson-Palmer approach to inverse Ising problems with quenched random fields
• On the large N limit of matrix integrals over the orthogonal group
• Non-linear susceptibilities of spherical models
• Statistical mechanical analysis of the linear vector channel in digital communication
• Directly observing replica symmetry breaking in a vector quantum-optical spin glass
• The replica-symmetric free energy for Ising spin glasses with orthogonally invariant couplings
• Critical slowing down exponents in quenched disordered spin models for structural glasses: Random Orthogonal and related models
• Typical $l_1$-recovery limit of sparse vectors represented by concatenations of random orthogonal matrices
• High Temperature Asymptotics of Orthogonal Mean-Field Spin Glasses
• Optimal Learning with Excitatory and Inhibitory synapses
• Low temperature spin glass fluctuations: expanding around a spherical approximation
• A study of the universal threshold in the L1 recovery by statistical mechanics