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We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all non-paramagnetic stationary points of the free energy are organized into pairs, consisting in a minimum and a saddle of…

Statistical Mechanics · Physics 2009-11-10 Andrea Cavagna , Irene Giardina , Giorgio Parisi

The overlap of the excited states in quasiparticle random-phase approximation (QRPA) is calculated in order to simulate the overlap of the intermediate nuclear states of the double-beta decay. Our basic idea is to use the like-particle QRPA…

Nuclear Theory · Physics 2015-06-11 J. Terasaki

Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of…

Disordered Systems and Neural Networks · Physics 2025-12-02 Kumar Ghosh

The supersymmetry self-consistent approximation for the model of non-equilibrium thermodynamic system with quenched disorder is derived from the dynamical action calculated by means of generalized second Legendre transformation. The…

Statistical Mechanics · Physics 2009-10-31 Alexei Kiselev

We study the consequences of supersymmetry breaking in the computation of the number of solutions of the Thouless-Anderson-Palmer (TAP) equations. We show that Kurchan argument that proves the vanishing of the prefactor of the Bray and…

Disordered Systems and Neural Networks · Physics 2012-10-31 G. Parisi , T. Rizzo

A theory for the complexity of the Bethe lattice spin-glass is developed applying to the cavity-method scheme of Mezard and Parisi the results recently obtained in the context of the Sherrington-Kirkpatrick model. The crucial ingredient is…

Disordered Systems and Neural Networks · Physics 2007-05-23 Tommaso Rizzo

Based on the modified Thouless-Anderson-Palmer equations a detailed numerical investigation for the complexity of the Sherrington-Kirkpatrick spin glass is worked out. The data suggest a scaling law which leads to a vanishing of the…

Disordered Systems and Neural Networks · Physics 2007-05-23 T. Plefka

The Complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising $p$-spin is investigated in the temperature regime where the equilibrium phase is one step Replica Symmetry Breaking. Two solutions of the resulting saddle point…

Statistical Mechanics · Physics 2016-08-31 A. Crisanti , L. Leuzzi , T. Rizzo

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

In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…

Mathematical Physics · Physics 2026-01-14 Francesco Camilli , Pierluigi Contucci , Emanuele Mingione , Daniele Tantari

In this paper we analyze the structure of the UNSAT-phase of the overconstrained 3-SAT model by studying the low temperature phase of the associated disordered spin model. We derive the $\infty$ Replica Symmetry Broken equations for a…

Statistical Mechanics · Physics 2009-11-07 A. Crisanti , L. Leuzzi , G. Parisi

The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…

Disordered Systems and Neural Networks · Physics 2015-10-27 Adriano Barra , Francesco Guerra , Emanuele Mingione

We consider algorithmic determination of the $n$-dimensional Sherrington-Kirkpatrick (SK) spin glass model ground state free energy. It corresponds to a binary maximization of an indefinite quadratic form and under the \emph{worst case}…

Disordered Systems and Neural Networks · Physics 2025-07-15 Mihailo Stojnic

We propose a new iterative construction of solutions of the classical TAP equations for the Sherrington-Kirkpatrick model, i.e. with finite-size Onsager correction. The algorithm can be started in an arbitrary point, and converges up to the…

Probability · Mathematics 2023-11-21 Stephan Gufler , Adrien Schertzer , Marius A. Schmidt

In this work we analyse the Parisi's infinity-replica symmetry breaking solution of the Sherrington - Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from…

Disordered Systems and Neural Networks · Physics 2009-11-07 A. Crisanti , T. Rizzo

We present a formalism for computing the complexity of metastable states and the zero-temperature magnetic hysteresis loop in the soft-spin random-field model in finite dimensions. The complexity is obtained as the Legendre transform of the…

Disordered Systems and Neural Networks · Physics 2015-05-20 M. L. Rosinberg , G. Tarjus

A scaling theory of replica symmetry breaking (RSB) in the SK-model is presented in the framework of critical phenomena for the scaling regime of small inverse RSB-orders, small temperatures, small magnetic fields, and near opposite…

Disordered Systems and Neural Networks · Physics 2009-11-13 Reinhold Oppermann , Manuel J. Schmidt

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

In these notes I will review the results that have been obtained in these last years on the computation of the number of metastable states in infinite-range models of disordered systems. This is a particular case of the problem of computing…

Disordered Systems and Neural Networks · Physics 2007-05-23 Giorgio Parisi

We investigate the large deviation behavior of the overlap probability density in the Sherrington--Kirkpatrick model from several analytical perspectives. First we analyze the spin glass phase using the coupled replica scheme. Here…

Statistical Mechanics · Physics 2009-11-07 Alain Billoire , Silvio Franz , Enzo Marinari