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Related papers: Universality in bipartite mean field spin glasses

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We compute analytically the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. we compute the exponentially small probability of finding a system with intensive…

Disordered Systems and Neural Networks · Physics 2012-10-31 Giorgio Parisi , Tommaso Rizzo

We consider vector spin glasses whose energy function is a Gaussian random field with covariance given in terms of the matrix of scalar products. For essentially any model in this class, we give an upper bound for the limit free energy,…

Probability · Mathematics 2021-12-06 Jean-Christophe Mourrat

We prove a duality principle that connects the thermodynamic limits of the free energies of the Hamiltonians and their squared interactions. Under the main assumption that the limiting free energy is concave in the squared temperature…

Probability · Mathematics 2017-05-23 Antonio Auffinger , Wei-Kuo Chen

We study numerically a disordered model that interpolates among the Sherrington-Kirkpatrick mean field model and the three dimensional Edwards-Anderson spin glass. We find that averages over the disorder of powers of the overlap and of the…

Disordered Systems and Neural Networks · Physics 2009-10-31 E. Marinari

Glasses are known to exhibit quantitative universalities at low temperatures, the most striking of which is the ultrasonic attenuation coefficient 1/Q. In this work we develop a theory of coupled generic blocks with a certain randomness…

Disordered Systems and Neural Networks · Physics 2015-05-27 Dervis C. Vural , Anthony J. Leggett

The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…

Disordered Systems and Neural Networks · Physics 2008-03-25 Helmut G. Katzgraber , Alexander K. Hartmann , A. P. Young

These lecture notes focus on the mean field theory of spin glasses, with particular emphasis on the presence of a very large number of metastable states in these systems. This phenomenon, and some of its physical consequences, will be…

Statistical Mechanics · Physics 2014-09-23 Francesco Zamponi

In this work we consider the {\em analog bipartite spin-glass} (or {\em real-valued restricted Boltzmann machine} in a neural network jargon), whose variables (those quenched as well as those dynamical) share standard Gaussian…

Disordered Systems and Neural Networks · Physics 2018-11-22 Elena Agliari , Francesco Alemanno , Adriano Barra , Alberto Fachechi

We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model and the one without an external field. We…

Disordered Systems and Neural Networks · Physics 2021-05-26 Jinho Baik , Elizabeth Collins-Woodfin , Pierre Le Doussal , Hao Wu

We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…

Mathematical Physics · Physics 2014-07-09 Gernot Akemann , Dario Villamaina , Pierpaolo Vivo

In this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one of a bipartite spin glass (whose parties consist of Ising and…

Disordered Systems and Neural Networks · Physics 2015-06-05 Adriano Barra , Giuseppe Genovese , Francesco Guerra , Daniele Tantari

We provide a strategy to find in few elementary calculations the critical exponents of the overlaps for dilute spin glasses, in absence of external field. Such a strategy is based on the expansion of a suitably perturbed average of the…

Statistical Mechanics · Physics 2007-10-25 Luca De Sanctis , Adriano Barra , Viola Folli

A recently introduced Renormalization Group approach to frustrated spin models is applied in three dimensions through Monte Carlo computations. A class of spin glass models is analysed, with correlated disorder variables given by a Z_2…

Statistical Mechanics · Physics 2007-05-23 Leonardo Gnesi , Roberto Petronzio , Francesco Rosati

This paper characterizes the annealed complexity of bipartite spherical spin glasses, both pure and mixed. This means we give exact variational formulas for the asymptotics of the expected numbers of critical points and of local minima.…

Probability · Mathematics 2023-03-22 Benjamin McKenna

This review presents various aspects of a mean-field spin glass model known as the p-spin spherical spin glass model, which has raised a lot of interest in the study of spin glasses, and also for its possible links with a mean-field theory…

Disordered Systems and Neural Networks · Physics 2008-02-03 A. Barrat

We demonstrate the universality of the gravitational classical deflection angle of massless particles through O(G^3) by studying the high-energy limit of full two-loop four-graviton scattering amplitudes in pure Einstein gravity as well as…

High Energy Physics - Theory · Physics 2020-07-22 Zvi Bern , Harald Ita , Julio Parra-Martinez , Michael S. Ruf

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some…

Mathematical Physics · Physics 2008-09-29 Michael Aizenman , Robert Sims , Shannon L. Starr

We consider relaxation of a rigid spin cluster in an elastic medium in the presence of the magnetic field. Universal simple expression for spin-phonon matrix elements due to local rotations of the lattice is derived. The equivalence of the…

Statistical Mechanics · Physics 2008-05-05 E. M. Chudnovsky , D. A. Garanin , R. Schilling

In this letter, we show that the formulae of Bray and Moore for the average logarithm of the number of metastable states in spin glasses can be obtained by calculating the partition function with $m$ coupled replicas with the symmetry among…

Condensed Matter · Physics 2009-10-28 Giorgio Parisi , Marc Potters

By means of enhanced Monte Carlo numerical simulations parallelized on GPU's we study the critical properties of the spin-glass-like model for the mode-locked glassy random laser, a $4$-spin model with complex spins with a global spherical…

Disordered Systems and Neural Networks · Physics 2023-05-31 Jacopo Niedda , Giacomo Gradenigo , Luca Leuzzi , Giorgio Parisi