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We study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T=0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field solution. In the limit $T\ll 1$ two regions can be…

Disordered Systems and Neural Networks · Physics 2011-02-28 A. Crisanti , C. De Dominicis

A Schwinger boson mean field theory is developed for spin liquids in a symmetric spin-orbital model in higher dimensions. Spin, orbital and coupled spin-orbital operators are treated equally. We evaluate the dynamic correlation functions…

Strongly Correlated Electrons · Physics 2009-11-07 Shun-Qing Shen , Guang-Ming Zhang

20 years ago, Bovier, Kurkova, and L\"owe [5] proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick model of spin glasses at high temperatures. In this paper we…

Probability · Mathematics 2022-05-31 Anton Bovier , Adrien Schertzer

In certain mean field models for spin glasses there occurs a one step replica symmetry breaking pattern. As an example of general $1/N$-corrections in such systems, the fluctuations in the internal energy are calculated. For this specific…

Condensed Matter · Physics 2009-10-28 Th. M. Nieuwenhuizen

Spin glass models involving multiple replicas with constrained overlaps have been studied in [FPV92; PT07; Pan18a]. For the spherical versions of these models [Ko19; Ko20] showed that the limiting free energy is given by a Parisi type…

Probability · Mathematics 2023-04-11 David Belius , Leon Fröber , Justin Ko

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

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 study a class of quantum spin systems in the mean-field setting of the complete graph. For spin $S=\tfrac12$ the model is the Heisenberg ferromagnet, for general spin $S\in\tfrac12\mathbb{N}$ it has a probabilistic representation as a…

Mathematical Physics · Physics 2019-12-16 J. E. Björnberg

While the Gibbs states of spin glass models have been noted to have an erratic dependence on temperature, one may expect the mean over the disorder to produce a continuously varying ``quenched state''. The assumption of such continuity in…

Statistical Mechanics · Physics 2015-06-25 M. Aizenman , P. Contucci

We study the equilibrium properties of an Ising frustrated lattice gas with a mean field replica approach. This model bridges usual {\em Spin Glasses} and a version of {\em Frustrated Percolation} model, and has proven relevant to describe…

Condensed Matter · Physics 2009-10-28 Jeferson J. Arenzon , Mario Nicodemi , Mauro Sellitto

We show marginal stability of near-ground states in spherical spin glasses is equivalent to full replica symmetry breaking at zero temperature near overlap $1$. This connection has long been implicit in the physics literature, which also…

Probability · Mathematics 2025-07-11 Mark Sellke

In this note, we consider a SK (Sherrington--Kirkpatrick)-type model on Z^d for d greater or equal to 1, weighted by a function allowing to any single spin to interact with a small proportion of the other ones. In the thermodynamical limit,…

Probability · Mathematics 2007-05-23 Sergio De Carvalho Bezerra , Samy Tindel

We present a large-scale simulation of the ground state interface properties of the diluted Sherrington-Kirkpatrick spin glass of Gaussian disorder for a broad range of the bond occupation probability $p$ using the strong disorder…

Disordered Systems and Neural Networks · Physics 2022-11-09 Wenlong Wang

We study numerically the out of equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low dimensional models.…

Condensed Matter · Physics 2009-10-22 L. F. Cugliandolo , J. Kurchan , F. Ritort

We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the…

Probability · Mathematics 2020-04-17 Gérard Ben Arous , Aukosh Jagannath

We discuss the issue of temperature chaos in the Sherrington--Kirkpatrick spin glass mean field model. We numerically compute probability distributions of the overlap among (equilibrium) configurations at two different values of the…

Disordered Systems and Neural Networks · Physics 2009-11-07 Alain Billoire , Enzo Marinari

In this short note, we prove a central limit theorem for the free energy in the Ghatak- Sherrington model at high enough temperatures, based on a generalization of the stochastic calculus method for the SK model derived in [CN95, Tin05].

Probability · Mathematics 2024-08-30 Yueqi Sheng

The Sherrington-Kirkpatrick Hamiltonian is a random quadratic function on the high-dimensional sphere. This article studies the ground state (i.e. maximum) of this Hamiltonian with external field, or more generally with a non-linear "spike"…

Probability · Mathematics 2023-07-28 David Belius , Leon Fröber

We consider the Sherrington--Kirkpatrick spin glass model with zero external field and at inverse temperature $\beta>0$. Let $F_N(\beta)$ be the corresponding log-partition function. Under the assumption that $c_N:=N^{1/3}(1-\beta_N^2)$ is…

Probability · Mathematics 2026-03-09 Partha S. Dey , Taegu Kang

Recently, Mori [Phys. Rev. E 84, 031128 (2011)] has conjectured that the free energy of Ising spin glass models with the Kac potential in the non-additive limit, such as the power-law potential in the non-additive regime, is exactly equal…

Disordered Systems and Neural Networks · Physics 2023-07-25 Manaka Okuyama , Masayuki Ohzeki