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We discuss the Sherrington-Kirkpatrick mean-field version of a spin glass within the distributional zeta-function method (DZFM). In the DZFM, since the dominant contribution to the average free energy is written as a series of moments of…

Disordered Systems and Neural Networks · Physics 2021-09-08 C. D. Rodríguez-Camargo , E. A. Mojica-Nava , N. F. Svaiter

In a companion paper we developed the generalized TAP approach for general multi-species spherical mixed $p$-spin models. In this paper, we use it to compute the limit of the free energy at any temperature for all pure multi-species…

Probability · Mathematics 2022-05-04 Eliran Subag

In these lectures I will review some theoretical results that have been obtained for spin glasses. I will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. I will…

Disordered Systems and Neural Networks · Physics 2007-06-04 Giorgio Parisi

A mean-field model of Ising spin glass with the Hamiltonian being a sum of the infinite-range ferromagnetic and random antiferromagnetic interactions is studied. It is shown that this model has phase transition in external magnetic field…

Disordered Systems and Neural Networks · Physics 2007-05-23 P. N. Timonin

The state space for the $N$-spin mean field (SK) spin glass--nominally an $N$-cube--is embedded in a low dimensional continuous space in such a way that metastable and stable phases can easily be discerned, a concept of nearness of…

Statistical Mechanics · Physics 2007-11-08 L. S. Schulman

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 study the 3-spin spherical model with mean-field interactions and Gaussian random couplings. For moderate system sizes of up to 20 spins, we obtain all stationary points of the energy landscape by means of the numerical polynomial…

Statistical Mechanics · Physics 2015-03-20 Dhagash Mehta , Daniel A. Stariolo , Michael Kastner

In the present paper we analyze the critical properties of a quantum spherical spin glass model with short range, random interactions. Since the model allows for rigorous detailed calculations, we can show how the effective partition…

Disordered Systems and Neural Networks · Physics 2008-06-10 Pedro Castro Menezes , Alba Theumann

We investigate the fluctuations of the free energy of the $2$-spin spherical Sherrington-Kirkpatrick model at critical temperature $\beta_c = 1$. When $\beta = 1$ we find asymptotic Gaussian fluctuations with variance $\frac{1}{6N^2}…

Probability · Mathematics 2024-06-19 Benjamin Landon

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

From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the…

Mathematical Physics · Physics 2010-07-26 Flora Koukiou

The spectra of spin models have been investigated in computation experiments. For the Sherrington-Kirkpatrick and Edwards-Anderson models we have determined the basic spectral characteristics: the average depth of a local minimum, the…

Disordered Systems and Neural Networks · Physics 2016-06-09 Boris Kryzhanovsky , Magomed Malsagov

A scheme to calculate the electronic structure of systems having a spiral magnetic structure is presented. The approach is based on the KKR (Korringa-Kohn-Rostoker) Green's function formalism which allows in combination with CPA (Coherent…

Strongly Correlated Electrons · Physics 2013-08-08 S. Mankovsky , G. H. Fecher , H. Ebert

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 study statistical properties of 3D classical spin glass layer of certain width and infinite length. The 3D spin glass is represented as an ensemble of disordered 1D spatial spin-chains (SSC) where interactions are random between…

Statistical Mechanics · Physics 2011-07-13 A. S. Gevorkyan , H. G. Abajyan , E. A. Ayryan

The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical…

Disordered Systems and Neural Networks · Physics 2023-07-19 Nicola Kistler , Marius Alexander Schmidt , Giulia Sebastiani

We construct and analyze a family of $M$-component vectorial spin systems which exhibit glass transitions and jamming within supercooled paramagnetic states without quenched disorder. Our system is defined on lattices with connectivity…

Statistical Mechanics · Physics 2018-06-27 Hajime Yoshino

We investigate magnetic properties of a two-dimensional periodic structure with Ising spins and antiferromagnetic nearest neighbor interaction. The structure is topologically equivalent to the Archimedean (3,12^2) lattice. The ground state…

Statistical Mechanics · Physics 2007-05-23 M. J. Krawczyk , K. Malarz , B. Kawecka-Magiera , A. Z. Maksymowicz , K. Kulakowski

It is presented a theory that describes a spin glass phase at finite temperatures in Kondo lattice systems with an additional RKKY interaction represented by long range, random couplings among localized spins like in the Sherrington-…

Statistical Mechanics · Physics 2009-10-31 Alba Theumann , B. Coqblin , S. G. Magalhaes , A. A. Schmidt

In this note we show how to generalize the stochastic calculus method introduced by Comets and Neveu [Comm. Math. Phys. 166 (1995) 549-564] for two models of spin glasses, namely, the SK model with external field and the perceptron model.…

Probability · Mathematics 2007-05-23 Samy Tindel