منابع مشابه
Rigorous Solution of a Mean Field Spin Glass Model
A separable spin glass model whose exchange integral takes the form Jij-J(ilj2+12jl) which was solved by van Hemmen et al. [12] using large deviation theory [14] is rigorously treated. The almost sure convergence criteria associated with the cumulant generating function C(t) with respect to the quenched random variables (is carefully investigated, and it is proved that the related excluded null...
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In this paper we analyze two main prototypes of disordered mean-field systems, namely the Sherrington-Kirkpatrick (SK) and the Viana-Bray (VB) models, to show that, in the framework of the cavity method, the transition from the annealed regime to a broken replica symmetry phase can be thought of as the failure of the saturability property (detailed explained along the paper) of the overlap fluc...
متن کاملDynamics within metastable states in a mean-field spin glass
In this letter we present a dynamical study of the structure of metastable states (corresponding to TAP solutions) in a mean-field spin–glass model. After reviewing known results of the statical approach, we use dynamics: starting from an initial condition thermalized at a temperature between the statical and the dynamical transition temperatures, we are able to study the relaxational dynamics ...
متن کاملMean field theory of a quantum heisenberg spin glass
A full mean-field solution of a quantum Heisenberg spin-glass model is presented in a large- N limit. A spin-glass transition is found for all values of the spin S. The quantum critical regime associated with the quantum transition at S = 0 and the various regimes in the spin-glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperature. In the spin-glass...
متن کاملMean-field theory for a spin-glass model of neural networks: TAP free energy and paramagnetic to spin-glass transition
An approach is proposed to the Hopfield model where the mean-field treatment is made for a given set of stored patterns (sample) and then the statistical average over samples is taken. This corresponds to the approach made by Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin glasses. Taking into account the fact that in the Hopfield model there exist correlations between d...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2019
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-019-03308-8