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We present a theory to describe the dynamics of the Sherrington- Kirkpatrick spin-glass with (sequential) Glauber dynamics in terms of deterministic flow equations for macroscopic parameters. Two transparent assumptions allow us to close…

Condensed Matter · Physics 2009-10-22 A. C. C Coolen , D. Sherrington

We consider the Sherrington-Kirkpatrick model and we prove that the thermodynamic limit of the quenched free energy per site is strictly greater than the corresponding replica symmetric approximation, for all values of the temperature and…

Disordered Systems and Neural Networks · Physics 2009-11-07 Fabio L. Toninelli

We study a spin system with both mixed even-spin Sherrington-Kirkpatrick (SK) couplings and Curie-Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the…

Probability · Mathematics 2012-12-03 Wei-Kuo Chen

We present a numerical study of the order-parameter fluctuations for Ising spin glasses in three and four dimensions at very low temperatures and without an external field. Accurate measurements of two previously introduced parameters, A…

Disordered Systems and Neural Networks · Physics 2009-11-10 Matteo Palassini , Marta Sales , Felix Ritort

We study finite-size corrections to the free energy of the Sherrington-Kirkpatrick spin glass in the low temperature phase. We investigate the role of longitudinal fluctuations in these corrections, neglecting the transverse contribution.…

Disordered Systems and Neural Networks · Physics 2019-05-01 Giorgio Parisi , Leopoldo Sarra , Lorenzo Talamanca

Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The…

Disordered Systems and Neural Networks · Physics 2008-07-09 Claudio Giberti , Cecilia Vernia

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

In the last five decades, mean-field neural-networks have played a crucial role in modelling associative memories and, in particular, the Hopfield model has been extensively studied using tools borrowed from the statistical mechanics of…

Disordered Systems and Neural Networks · Physics 2024-09-17 Elena Agliari , Adriano Barra , Pierluigi Bianco , Alberto Fachechi , Diego Pallara

The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a closed-form generating functional. We first find an integral representation for a solution of the Parisi differential equation and represent the…

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

As Phil Anderson noted long ago, frustration can be generally defined by measuring the fluctuations in the coupling energy across a plane boundary between two large blocks of material. Since that time, a number of groups have studied the…

Disordered Systems and Neural Networks · Physics 2014-08-12 D. L. Stein

A generalization of the Sherrington-Kirkpatrick (SK) model for spin glasses is considered, in which the interaction matrix is endowed with a variance profile that has no particular structure an may be sparse. In the first part of this…

Mathematical Physics · Physics 2026-04-29 Walid Hachem

We generalize the strategy, we recently introduced to prove the existence of the thermodynamic limit for the Sherrington-Kirkpatrick and p-spin models, to a wider class of mean field spin glass systems, including models with multi-component…

Disordered Systems and Neural Networks · Physics 2007-05-23 Francesco Guerra , Fabio L. Toninelli

In this paper we study the equilibrium statistical mechanical as well as the dynamical properties of a Sherrington and Kirkpatrick model in a multi-bath setting introduced in [4]. We show that the free energy per particle in the…

Disordered Systems and Neural Networks · Physics 2019-09-04 Pierluigi Contucci , Jorge Kurchan , Emanuele Mingione

In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function $\sigma:[0,1]^4\to\{-1,+1\}$, and one can…

Probability · Mathematics 2013-05-27 Dmitry Panchenko

We develop further a recent dynamical replica theory to describe the dynamics of the Sherrington-Kirkpatrick spin-glass in terms of closed evolution equations for macroscopic order parameters. We show how microscopic memory effects can be…

Condensed Matter · Physics 2009-10-28 S. N. Laughton , A. C. C. Coolen , D. Sherrington

We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…

Probability · Mathematics 2023-04-27 Ratul Biswas , Wei-Kuo Chen , Arnab Sen

We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi…

Probability · Mathematics 2018-03-28 Dmitry Panchenko

For large but finite systems the static properties of the infinite ranged Sherrington-Kirkpatrick model are numerically investigated in the entire the glass regime. The approach is based on the modified Thouless-Anderson-Palmer equations in…

Disordered Systems and Neural Networks · Physics 2019-07-18 T. Plefka

We study properties of the energy minima obtained by quenching equilibrium configurations of the Sherrington-Kirkpatrick (SK) mean field spin glass. We measure the probability distribution of the overlap among quenched configurations and…

Disordered Systems and Neural Networks · Physics 2007-05-23 Barbara Coluzzi , Enzo Marinari , Giorgio Parisi , Heiko Rieger

We address the problem of chaotic temperature dependence in disordered glassy systems at equilibrium by following states of a random-energy random-entropy model in temperature; of particular interest are the crossings of the free-energies…

Disordered Systems and Neural Networks · Physics 2015-06-24 F. Krzakala , O. C. Martin