相关论文: On the TAP approach to the spherical p-spin SG mod…

We compute the free energy at all temperatures for the spherical pure $p$-spin models from the generalized Thouless-Anderson-Palmer representation. This is the first example of a mixed $p$-spin model for which the free energy is computed in…

We solve the Thouless-Anderson-Palmer (TAP) variational principle associated to the spherical pure $p$-spin mean field spin glass Hamiltonian and present a detailed phase diagram. In the high temperature phase the maximum of variational…

We develop a generalized TAP approach for the multi-species version of the spherical mixed $p$-spin models. In particular, we prove a generalized TAP representation for the free energy at any overlap vector which is multi-samplable in an…

In the context of the p-spin spherical model, we introduce a method for the computation of the number of stationary points of any nature (minima, saddles, etc.) of the TAP free energy. In doing this we clarify the ambiguities related to the…

This work proves an upper bound for the free energy of the Sherrington-Kirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to models with spherical or Ising spins and any mixed…

We study a quantum extension of the spherical $p$-spin-glass model using the imaginary-time replica formalism. We solve the model numerically and we discuss two analytical approximation schemes that capture most of the features of the…

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field $D$ for a large number of spins. This…

We consider the mixed $p$-spin mean-field spin glass model with Ising spins and investigate its free energy in the spirit of the TAP approach, named after Thouless, Anderson, and Palmer. More precisely, we define and compute the generalized…

The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical…

In a recent paper [14], we developed the generalized TAP approach for mixed $p$-spin models with Ising spins at positive temperature. Here we extend these results in two directions. We find a simplified representation for the energy of the…

In a companion paper we developed the generalized TAP approach for general multi-species spherical mixed $p$-spin models. In this paper, we use it to compute the limit of the free energy at any temperature for all pure multi-species…

We discuss level crossing of the free-energy of TAP solutions under variations of external parameters such as magnetic field or temperature in mean-field spin-glass models that exhibit one-step Replica-Symmetry-Breaking (1RSB). We study the…

Spin glass models involving multiple replicas with constrained overlaps have been studied in [FPV92; PT07; Pan18a]. For the spherical versions of these models [Ko19; Ko20] showed that the limiting free energy is given by a Parisi type…

The number $\langle N_s\rangle$ 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 Thouless, Anderson, Palmer (TAP) approach to thermodynamics of mean field spin-glasses is generalised to dynamics. A method to compute the dynamical TAP equations is developed and applied to the p-spin spherical model. In this context…

The replica method has been used to calculate the interface free energy associated with the change from periodic to anti-periodic boundary conditions in finite-dimensional p-spin glass models in the phase which at mean-field level has…

We study the Hopfield model with pure $p$-spin interactions with even $p\geq 4$, and a number of patterns, M(N) growing with the system size, $N$, as $M(N) = \a N^{p-1}$. We prove the existence of a critical temperature $\b_p$ characterized…

We derive the TAP equations for the fermionic Ising spin glass. It is found that, just as in the non-fermionic model, the conditions for stability and for validity of the free energy are equivalent. We determine the breakdown of the…

We analyze the low-temperature behavior of mean-field equations of Thouless, Anderson, and Palmer (TAP). We demonstrate that degeneracy in free energy makes the low-temperature TAP states unstable. Different solutions of the TAP equations,…

We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…