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We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full…

Disordered Systems and Neural Networks · Physics 2015-06-12 Francesco Guerra

We establish three equivalent versions of a Parisi formula for the free energy of mean-field spin glasses in a transversal magnetic field. These results are derived from available results for classical vector spin glasses by an…

Disordered Systems and Neural Networks · Physics 2024-03-12 Chokri Manai , Simone Warzel

A detailed numerical study is made of relaxation at equilibrium in the Sherrington-Kirkpatrick Ising spin glass model, at and above the critical temperature Tg. The data show a long time stretched exponential relaxation q(t) ~…

Disordered Systems and Neural Networks · Physics 2015-05-28 Alain Billoire , I. A. Campbell

The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking…

Disordered Systems and Neural Networks · Physics 2007-05-23 D. S. Dean , F. Ritort

We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at zero temperature upon small changes in the magnetic field. For the infinite-range Sherrington-Kirkpatrick model we present a detailed…

Disordered Systems and Neural Networks · Physics 2013-05-30 Pierre Le Doussal , Markus Mueller , Kay Joerg Wiese

We propose and demonstrate numerically a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model, employing the Suzuki-Kubo meanfield Ising dynamics (supplemented by a modified Thouless-Anderson-Palmer reaction…

Disordered Systems and Neural Networks · Physics 2025-06-18 Soumyaditya Das , Soumyajyoti Biswas , Bikas K. Chakrabarti

In this paper, we will investigate critical phenomena by considering a model spin-glass on scale-free networks. For this purpose, we consider the Ghatak-Sherrington (GS) model, a spin-1 spin-glass model with a crystal field, instead of the…

Disordered Systems and Neural Networks · Physics 2014-03-14 Do-Hyun Kim

We calculate the probability distribution of the overlap between a spin glass and a copy of itself in which the bonds are randomly perturbed in varying degrees. The overlap distribution is shown to go to a delta distribution in the…

Disordered Systems and Neural Networks · Physics 2008-05-05 T. Aspelmeier

Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and…

Disordered Systems and Neural Networks · Physics 2014-10-29 Matthew Wittmann , B. Yucesoy , Helmut G. Katzgraber , J. Machta , A. P. Young

We explore the behavior of order parameter distribution of quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamil- tonian at finite temperatures and that at zero…

Statistical Mechanics · Physics 2018-03-01 Sudip Mukherjee , Atanu Rajak , Bikas K Chakrabarti

This paper studies spin glass to paramagnetic transition in the Spherical Sherrington-Kirkpatrick model with ferromagnetic Curie-Weiss interaction with coupling constant $J$ and inverse temperature $\beta$. The disorder of the system is…

Probability · Mathematics 2024-08-26 Iain M. Johnstone , Yegor Klochkov , Alexei Onatski , Damian Pavlyshyn

We study numerically the Sherrington--Kirkpatrick model as function of the magnetic field h, with fixed temperature T=0.6 Tc. We investigate the finite size scaling behavior of several quantities, such as the spin glass susceptibility,…

Statistical Mechanics · Physics 2009-11-10 Alain Billoire , Barbara Coluzzi

In this note, we consider the multi-species Sherrington-Kirkpatrick spin glass model at its conjectured critical temperature, and we show that, when the variance profile matrix $\Delta^2$ is positive semi-definite, the variance of the free…

Probability · Mathematics 2025-01-22 Elizabeth Collins-Woodfin , Han Gia Le

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

Within the replica approach to mean-field spin-glasses the transition from ergodic high-temperature behaviour to the glassy low-temperature phase is marked by the instability of the replica-symmetric saddle-point. For general spin-glass…

Disordered Systems and Neural Networks · Physics 2015-05-19 Katharina Janzen , Andreas Engel

We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short range Ising spin glass (3dISG). For the SK model, evidence for ultrametricity becomes clearer as the system size…

Disordered Systems and Neural Networks · Physics 2007-05-23 Guy Hed , A. P. Young , Eytan Domany

We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures $\beta>0$. To characterize the free energy,…

Probability · Mathematics 2020-01-01 Arka Adhikari , Christian Brennecke

By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a transverse magnetic field if the temperature…

Disordered Systems and Neural Networks · Physics 2021-11-16 Hajo Leschke , Chokri Manai , Rainer Ruder , Simone Warzel

Disordered systems generically exhibit aging and a glass transition. Previous studies have long suggested that non-reciprocity tends to destroy glassiness. Here, we show that this is not always the case using a bipartite spherical…

Disordered Systems and Neural Networks · Physics 2025-11-11 Giulia Garcia Lorenzana , Ada Altieri , Giulio Biroli , Michel Fruchart , Vincenzo Vitelli

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