On the formal equivalence of the TAP and thermodynamic methods in the SK model (original) (raw)

Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses

Journal of Physics A-mathematical and General, 2004

The structure of states of the perturbed p-spin spherical spin-glass is analyzed. At low enough free energy metastable states have a supersymmetric structure, while at higher free energies the supersymmetry is broken. The transition between the supersymmetric and the supersymmetry-breaking phase is triggered by a change in the stability of states.

Course 7 Computing the number of metastable states in infinite-range models

Les Houches, 2006

Course 7 COMPUTING THE NUMBER OF METASTABLE STATES IN INFINITE-RANGE MODELS Giorgio Parisi Dipartimento di Fisica, INFM, SMC and INFN, Universitdi Roma La Sapienza, PA Moro 2, 00185 Rome, Italy A. Bovier, F. Dunlop, F. den Hollander, A. van Enter and J. Dalibard, eds. Les Houches, Session LXXXIII, 2005 Mathematical Statistical Physics 006 Elsevier BV All rights reserved 295 Content 1. Introduction 299 2. The TAP equations 303 3. A simple analysis of the solutions of the Bethe equations 307 4. The direct ...

Quenched computation of the dependence of complexity on the free energyin the Sherrington-Kirkpatrick model

Physical Review B, 2004

The frozen phase of mean field spin glass models displays, in the thermodynamic limit, a very high number of stable and metastable states. Such a feature is the consequence of the disorder and the frustration characterizing spin glasses and causing the onset of many different configurations of spins minimizing the thermodynamic potential, organized in the phase space in a rather complicated way. In order to comprehend the structure of the landscape of the thermodynamic potential below a given critical temperature a very ...

Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry

arXiv: Statistical Mechanics, 2020

We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction (Whitney's problem). Considered on the entire time axis, the problem admits a unique solution that always remains in the upper half plane. We formulate the problem of statistical description of this never-falling trajectory and solve it by a field-theoretical technique assuming a white-noise driving. In our approach based on the supersymmetric formalism of Parisi and Sourlas, statistic properties of the never-falling trajectory are expressed in terms of the zero mode of the corresponding transfer-matrix Hamiltonian. The emerging mathematical structure is similar to that of the Fokker-Planck equation, which however is written for the ``square root'' of the probability distribution function. Our results for the statistics of the non-falling trajectory are in perfect agreement with direct numerical simulations of the stochastic pendulum equation. In the limit of strong...

Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory

We study localization of five-dimensional supersymmetric U(1)U(1)U(1) gauge theory on mathbbS3timesmathbbRtheta2\mathbb{S}^3 \times \mathbb{R}_{\theta}^{2}mathbbS3timesmathbbRtheta2 where mathbbRtheta2\mathbb{R}_{\theta}^{2}mathbbRtheta2 is a noncommutative (NC) plane. The theory can be isomorphically mapped to three-dimensional supersymmetric U(Ntoinfty)U(N \to \infty)U(Ntoinfty) gauge theory on mathbbS3\mathbb{S}^3mathbbS3 using the matrix representation on a separable Hilbert space on which NC fields linearly act. Therefore the NC space mathbbRtheta2\mathbb{R}_{\theta}^{2}mathbbRtheta2 allows for a flexible path to derive matrix models via localization from a higher-dimensional supersymmetric NC U(1)U(1)U(1) gauge theory. The result shows a rich duality between NC U(1)U(1)U(1) gauge theories and large NNN matrix models in various dimensions.