# The Generalized TAP Free Energy II

@article{Chen2019TheGT, title={The Generalized TAP Free Energy II}, author={Wei-Kuo Chen and Dmitry Panchenko and Eliran Subag}, journal={Communications in Mathematical Physics}, year={2019}, volume={381}, pages={257-291} }

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…

## 26 Citations

### Generalized TAP Free Energy

- MathematicsCommunications on Pure and Applied Mathematics
- 2022

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

- Physics
- 2022

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

- Mathematics
- 2022

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

- Physics
- 2022

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

- Mathematics
- 2021

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

- Mathematics
- 2022

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

- Physics
- 2022

. 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

- Computer Science, Mathematics
- 2022

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

- Physics
- 2021

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

- PhysicsJournal of Mathematical Physics
- 2021

, 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…

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