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Related papers: Quantum TAP equations

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We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, $\langle\cdot\rangle_N$, into a…

Probability · Mathematics 2020-04-17 Antonio Auffinger , Aukosh Jagannath

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,…

Disordered Systems and Neural Networks · Physics 2008-09-16 V. Janis

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…

Disordered Systems and Neural Networks · Physics 2009-10-31 Giulio Biroli

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…

Condensed Matter · Physics 2009-10-22 H. Rieger

The spherical mean field approximation of a spin-1 model with p-body quenched disordered interaction is investigated. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the…

Disordered Systems and Neural Networks · Physics 2012-03-06 Ulisse Ferrari , Luca Leuzzi

We derive the Thouless-Anderson-Palmer (TAP) equations for the Ghatak and Sherrington model. Our derivation, based on the cavity method, holds at high temperature and at all values of the crystal field. It confirms the prediction of Yokota.

Probability · Mathematics 2021-09-01 Antonio Auffinger , Cathy Xi Chen

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…

Disordered Systems and Neural Networks · Physics 2022-07-07 David Belius , Marius A. Schmidt

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…

Disordered Systems and Neural Networks · Physics 2009-10-31 Leticia F Cugliandolo , D. R. Grempel , Constantino A da Silva Santos

We present a new dynamical proof of the Thouless-Anderson-Palmer (TAP) equations for the classical Sherrington-Kirkpatrick spin glass at sufficiently high temperature. In our derivation, the TAP equations are a simple consequence of the…

Mathematical Physics · Physics 2021-08-02 Arka Adhikari , Christian Brennecke , Per von Soosten , Horng-Tzer Yau

In this letter we analyze the TAP approach to the spherical $p$-spin spin glass model in zero external field. The TAP free energy is derived by summing up all the relevant diagrams for $N\to\infty$ of a diagrammatic expansion of the free…

Condensed Matter · Physics 2007-05-23 A. Crisanti , H. -J. Sommers

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 equations, originally derived by Parisi…

Probability · Mathematics 2022-12-22 Zhou Fan , Yufan Li , Subhabrata Sen

We revisit the metastability properties of the mixed p-spin spherical disordered models. Firstly, using known methods, we show that there is temperature chaos in a broad range of temperatures. Secondly, we modify the definition of the…

Disordered Systems and Neural Networks · Physics 2020-08-26 Damien Barbier , Leticia Cugliandolo

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…

Disordered Systems and Neural Networks · Physics 2012-10-31 Tommaso Rizzo , Hajime Yoshino

We prove the Thouless-Anderson-Palmer (TAP) equations for the local magnetization in the multi-species Sherrington-Kirkpatrick (MSK) spin glass model. One of the key ingredients is based on concentration results established…

Probability · Mathematics 2023-08-21 Qiang Wu

We study analytically the dynamics of a generalized p-spin model, starting with a thermalized initial condition. The model presents birth and death of states, hence the dynamics (even starting at equilibrium) may go out of equilibrium when…

Disordered Systems and Neural Networks · Physics 2009-11-11 Barbara Capone , Tommaso Castellani , Irene Giardina , Federico Ricci-Tersenghi

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…

Disordered Systems and Neural Networks · Physics 2007-05-23 Martin Rehker , Reinhold Oppermann

We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small finite rate. We demonstrate that this model supports a first-order dynamical…

Statistical Mechanics · Physics 2010-10-14 Yael S. Elmatad , Robert L. Jack , Juan P. Garrahan , David Chandler

Chaotic quantum systems with Lyapunov exponent $\lambda_\mathrm{L}$ obey an upper bound $\lambda_\mathrm{L}\leq 2\pi k_\mathrm{B}T/\hbar$ at temperature $T$, implying a divergence of the bound in the classical limit $\hbar\to 0$. Following…

Disordered Systems and Neural Networks · Physics 2022-03-23 Surajit Bera , K. Y. Venkata Lokesh , Sumilan Banerjee

We consider the infinite-range deterministic spin models with Hamiltonian $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the quantization of a chaotic map of the torus. The mean field (TAP) equations are derived by summing the…

Condensed Matter · Physics 2009-10-28 I. Borsari , M. Degli esposti , S. Graffi , F. Unguendoli

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) spin glass model. The solutions to their…

Probability · Mathematics 2024-03-26 Wei-Kuo Chen , Si Tang
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