The Generalized TAP Free Energy II

  title={The Generalized TAP Free Energy II},
  author={Wei-Kuo Chen and Dmitry Panchenko and Eliran Subag},
  journal={Communications in Mathematical Physics},
In a recent paper (Chen et al. in The generalized TAP free energy, to appear in Comm. Pure Appl. Math.), 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 generalized TAP states in terms of the Parisi measure of the model and, in particular, show that the energy of all states at a given distance from the origin is the same… 

Generalized TAP Free Energy

In this paper, we define and compute the generalized TAP correction for the energy of the mixed p-spin models with Ising spins, and give the corresponding generalized TAP representation for the free

On the TAP equations via the cavity approach in the generic mixed $p$-spin models

In 1977, Thouless, Anderson, and Palmer (TAP) derived a system of consistent equations in terms of the effective magnetization in order to study the free energy in the Sherrington-Kirkpatrick (SK)

On the REM approximation of TAP free energies

Abstract. 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

High temperature TAP upper bound for the free energy of mean field spin glasses

Abstract. This work proves an upper bound for the free energy of the SherringtonKirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to

TAP approach for multi-species spherical spin glasses I: general theory

Abstract. 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

TAP equations for orthogonally invariant spin glasses at high temperature

We study the high-temperature regime of a mean-field spin glass model whose couplings matrix is orthogonally invariant in law. The magnetization of this model is conjectured to satisfy a system of TAP

Phase diagram for the tap energy of the $p$-spin spherical mean field spin glass model

. 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.Inthe high

The TAP free energy for high-dimensional linear regression

This work rigorously establishes the Thouless-Anderson-Palmer (TAP) approximation arising from spin glass theory, and proves a conjecture of [23] in the special case of the spherical prior (at sufficiently high temperature).

The free energy of spherical pure $p$-spin models -- computation from the TAP approach

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

Concentration of the complexity of spherical pure p-spin models at arbitrary energies

, and Ji1,...,ip are i.i.d standard normal variables. The model was introduced by Crisanti and Sommers [CS92] for general p ≥ 2 as a continuous variant of the same models with Ising spins, while for



On the TAP Free Energy in the Mixed p-Spin Models

Thouless et al. (Phys Mag 35(3):593–601, 1977), derived a representation for the free energy of the Sherrington–Kirkpatrick model, called the TAP free energy, written as the difference of the energy

Free energy in the mixed p-spin models with vector spins

Using the synchronization mechanism developed in the previous work on the Potts spin glass model, arXiv:1512.00370, we obtain the analogue of the Parisi formula for the free energy in the mixed even

On the energy landscape of the mixed even p-spin model

We investigate the energy landscape of the mixed even p-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming

Complexity in mean-field spin-glass models: Ising p-spin

The complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising $p$-spin is investigated in the temperature regime where the equilibrium phase is one-step replica symmetry breaking. Two

Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

Abstract: By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick

Free energy in the Potts spin glass

We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are

Chaos in the Mixed Even-Spin Models

We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the

Chaos in Temperature in Generic 2p-Spin Models

We prove chaos in temperature for even p-spin models which include sufficiently many p-spin interaction terms. Our approach is based on a new invariance property for coupled asymptotic Gibbs

Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime

We study the Gibbs measure of mixed spherical p‐spin glass models at low temperature, in (part of) the 1‐RSB regime, including, in particular, models close to pure in an appropriate sense. We show

The Parisi formula for mixed $p$-spin models

The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed $p$-spin models for even $p\geq2$ was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006)