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We calculate the real-time-correlation function of the Sherrington-Kirkpatrick spin-glass model in a transverse field. Using a careful analysis of the perturbative expansion of the functional-integral representation, we derive the…

Disordered Systems and Neural Networks · Physics 2008-11-19 Kazutaka Takahashi , Koujin Takeda

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 study the complexity of the Thouless-Anderson-Palmer (TAP) free energy for Ising spin glasses with a general mixed p-spin covariance, working with the generalized TAP functional of Chen, Panchenko, and Subag. We formulate three…

Probability · Mathematics 2026-04-24 Jeanne Boursier

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica…

Disordered Systems and Neural Networks · Physics 2009-04-30 D. B. Liarte , S. R. Salinas , C. S. O. Yokoi

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 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

We develop a simple method to study the high temperature, or high external field, behavior of the Sherrington-Kirkpatrick mean field spin glass model. The basic idea is to couple two different replicas with a quadratic term, trying to push…

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

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an…

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

We study the annealed complexity of the m-vector spin glasses in the Sherrington-Kirkpatrick limit. The eigenvalue spectrum of the Hessian matrix of the Thouless-Anderson-Palmer (TAP) free energy is found to consist of a continuous band of…

Disordered Systems and Neural Networks · Physics 2009-11-10 J. Yeo , M. A. Moore

The microscopic probability distribution function of the Sherrington-Kirkpatrick (SK) model of spin glasses is calculated explicitly as a function of time by a high-temperature expansion. The resulting formula to the third order of the…

Condensed Matter · Physics 2009-10-28 Hidetoshi Nishimori , Michiko Yamana

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 study a fermionic version of the Sherrington-Kirkpatrick model including nearest-neighbor hopping on a $\infty$-dimensional simple cubic lattices. The problem is reduced to one of free fermions moving in a dynamical effective random…

Disordered Systems and Neural Networks · Physics 2009-11-10 M. Bechmann , R. Oppermann

Asynchronous dynamics given by the master equation in the Sherrington--Kirkpatrick (SK) spin-glass model is studied based on dynamical replica theory (DRT) with an extension to take into account the autocorrelation function. The dynamical…

Disordered Systems and Neural Networks · Physics 2015-06-12 Ayaka Sakata

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

We discuss a general formalism that allows study of transitions over barriers in spin glasses with long-range interactions that contain large but finite number, $N$, of spins. We apply this formalism to the Sherrington-Kirkpatrick model…

Disordered Systems and Neural Networks · Physics 2009-10-30 L. B. Ioffe , D. Sherrington

The distribution of solutions of the Thouless-Anderson-Palmer equation is studied by extensive numerical experiments for fully connected 3-body interaction Ising spin glass models in a level of annealed calculation. A recent study predicted…

Disordered Systems and Neural Networks · Physics 2015-06-25 Yukinori Tonosaki , Koujin Takeda , Yoshiyuki Kabashima

We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) equations of Ising models with arbitrary rotation invariant (random) coupling matrices. In the thermodynamic limit, we prove by means of the dynamical…

Disordered Systems and Neural Networks · Physics 2019-07-03 Burak Çakmak , Manfred Opper

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

We develop a systematic expansion method of physical quantities for the SK model and the finite-dimensional $\pm J$ model of spin glasses in non-equilibrium states. The dynamical probability distribution function is derived from the master…

Disordered Systems and Neural Networks · Physics 2009-10-30 Michiko Yamana , Hidetoshi Nishimori , Tadashi Kadowaki , D. Sherrington

The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. A new alternative…

Disordered Systems and Neural Networks · Physics 2009-11-07 T. Plefka