Number of solutions of the TAP equations for p--spin interaction spin glasses

Abstract

The number $⟨N_s⟩$ of solutions of the equations of Thouless, Anderson and Palmer for p--spin interaction spin glass models is calculated. Below a critical temperature $T_c$ this number becomes exponentially large, as it is in the SK--model ($p=2$). But in contrast to this, for any $p>2$ the factor $\alpha (T)=N^{-1}\ln ⟨N_s⟩$ jumps discontinuously at $T_c(p)$, which is consistent with the discontinuity occuring within the mean--field theory for these models. For zero temperature the results obtained by Gross and Mézard are reproduced, and for $p\to \infty$ one gets the result for the random energy model.

arXiv comment13 pages + 2 figures (postscript files included!), needs REVTEX

Cited by in corpus (33)

• Supercooled Liquids for Pedestrians
• Spin-Glass Theory for Pedestrians
• On the stationary points of the TAP free energy
• Metastable states in glassy systems
• Mean-Field Equations for Spin Models with Orthogonal Interaction Matrices
• Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses
• Quantum TAP equations
• Complexity in Mean-Field Spin-Glass Models: Ising $p$-spin
• Quenched complexity of the p-spin spherical spin-glass with external magnetic field
• Dynamical TAP approach to mean field glassy systems
• On the number of metastable states in spin glasses
• On Spin-Glass Complexity
• Classical Glasses, Black Holes, and Strange Quantum Liquids
• Thermodynamic description of a dynamical glassy transition
• Dynamical Instantons and Activated Processes in Mean-Field Glass Models
• How to count in hierarchical landscapes: a 'full' solution to mean-field complexity
• Crossover from entropic to thermal dynamics in glassy models
• Relaxation dynamics of the Ising $p$-spin disordered model with finite number of variables
• Non equilibrium dynamics of isolated disordered systems: the classical Hamiltonian p-spin model
• Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses
• Landscape statistics of the p-spin Ising model
• The p-spin spherical spin glass model
• Barriers, trapping times and overlaps between local minima in the dynamics of the disordered Ising $p$-spin Model
• Tap Complexity, the Cavity Method and Supersymmetry
• Large deviations of glassy effective potentials
• The number of metastable states in the generalized random orthogonal model
• Message-passing algorithm of quantum annealing with nonstoquastic Hamiltonian
• Theory of simple glasses
• Role of free energy landscape in the dynamics of mean field glassy systems
• A constrained TAP approach for disordered spin models: application to the mixed spherical case
• Thouless-Anderson-Palmer equation and self-consistent signal-to-noise analysis for the Hopfield model with three-body interaction
• Complexity as the driving force for glassy transitions
• Recent theories of glasses as out of equilibrium systems