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Related papers: Low temperature solution of the Sherrington-Kirkpa…

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A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…

Condensed Matter · Physics 2009-10-22 Th. M. Nieuwenhuizen

By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…

Disordered Systems and Neural Networks · Physics 2007-05-23 Francesco Guerra

We investigate generalized Sherrington--Kirkpatrick glassy systems without reflection symmetry. In the neighbourhood of the transition temperature we in general uncover the structure of the glass state building the full-replica-symmetry…

Statistical Mechanics · Physics 2014-05-02 T. I. Schelkacheva , E. E. Tareyeva , N. M. Chtchelkatchev

Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB-steps playing a role of decimation scales, we report evidence for a non-trivial…

Disordered Systems and Neural Networks · Physics 2009-11-11 R. Oppermann , D. Sherrington

We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero field limit the system exactly realizes the…

Disordered Systems and Neural Networks · Physics 2015-01-16 Pietro Rotondo , Enrico Tesio , Sergio Caracciolo

We present a systematic and exact way of computing finite size corrections for the random energy model, in its low temperature phase. We obtain explicit (though complicated) expressions for the finite size corrections of the overlap…

Disordered Systems and Neural Networks · Physics 2015-06-23 Bernard Derrida , Peter Mottishaw

Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with…

Disordered Systems and Neural Networks · Physics 2015-03-13 Heinz Horner

We solve the fermionic version of the Ising spin glass for arbitrary filling \mu and temperature T taking into account replica symmetry breaking. Using a simple exact mapping from \mu to the anisotropy parameter D, we also obtain the…

Statistical Mechanics · Physics 2009-10-31 H. Feldmann , R. Oppermann

In the Sherrington-Kirkpatrick (SK) and related mixed $p$-spin models, there is interest in understanding replica symmetry breaking at low temperatures. For this reason, the so-called AT line proposed by de Almeida and Thouless as a…

Probability · Mathematics 2025-07-09 Erik Bates , Leila Sloman , Youngtak Sohn

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 the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…

Disordered Systems and Neural Networks · Physics 2015-06-24 Václav Janiš

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 obtain an exact analytic expression for the average distribution, in the thermodynamic limit, of overlaps between two copies of the same random energy model (REM) at different temperatures. We quantify the non-self averaging effects and…

Disordered Systems and Neural Networks · Physics 2021-02-03 Bernard Derrida , Peter Mottishaw

We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…

Disordered Systems and Neural Networks · Physics 2009-10-31 L. B. Ioffe , A. V. Lopatin

In this paper we study the bipartite version of Sherrington-Kirkpatrick model. We prove that the free energy density is given by an analogue of the Parisi formula, that contains both the usual overlap and an additional new type of overlap.…

Disordered Systems and Neural Networks · Physics 2018-12-18 Liming Pan , Simone Franchini

We study the Replica Symmetric region of general multi-species Sherrington-Kirkpatrick (MSK) Model and answer some of the questions raised in Ann.~Probab.~43~(2015), no.~6, 3494--3513, where the author proved the Parisi formula under…

Probability · Mathematics 2021-11-24 Partha S. Dey , Qiang Wu

In this paper we adapt the broken replica interpolation technique (developed by Francesco Guerra to deal with the Sherrington-Kirkpatrick model, namely a pairwise mean-field spin-glass whose couplings are i.i.d. standard Gaussian variables)…

Mathematical Physics · Physics 2020-06-02 Elena Agliari , Linda Albanese , Adriano Barra , Gabriele Ottaviani

We construct the first complete exact numerical solution of a mean field quantum spin glass model, the transverse field Sherrington-Kirkpatrick model, by implementing a continuous-time quantum Monte Carlo method in the presence of full…

Disordered Systems and Neural Networks · Physics 2025-04-08 Annamária Kiss , Gergely Zaránd , Izabella Lovas

We study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e. the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the…

Statistical Mechanics · Physics 2017-09-20 A. P. Young

In this paper, we study the high temperature or low connectivity phase of the Viana-Bray model. This is a diluted version of the well known Sherrington-Kirkpatrick mean field spin glass. In the whole replica symmetric region, we obtain a…

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