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Related papers: Free energy barriers in the Sherrington-Kirkpatric…

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Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…

Disordered Systems and Neural Networks · Physics 2024-05-24 Ho Fai Po , Chi Ho Yeung

We prove the convergence in distribution of the fluctuations of the free energy of the mixed $p$-spin Sherrington-Kirkpatrick model with non-vanishing $2$-spin component at high enough temperature. The limit is Gaussian, and the…

Probability · Mathematics 2021-08-09 Debapratim Banerjee , David Belius

All ground states and low-lying excitations of a +/- I Ising spin glass model on a cubic 4 x 4 x 4 lattice with periodical boundary conditions were calculated using a method of combinatorical optimization. The structure of states in the…

Condensed Matter · Physics 2016-08-31 T. Klotz , S. Kobe

We study the competition between ferromagnetic and spin glass phases using a system of coupled infinite-range Ising and Sherrington-Kirkpatrick models. We obtain the replica-symmetric solution for the free energy of this system in terms of…

Disordered Systems and Neural Networks · Physics 2023-06-28 Fateme Izadi , Reza Sepehrinia

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 consider energy relaxation of the long-range spin glass model with sparse couplings, the so-called dilute Sherrington-Kirkpatrick (SK) model, starting from a random initial state. We consider the effect that modularity of the coupling…

Statistical Mechanics · Physics 2014-01-21 Jeong-Man Park , Michael W. Deem

We show that the limiting free energy in Sherrington-Kirkpatrick's Spin Glass Model does not depend on the environment.

Probability · Mathematics 2007-05-23 Philippe Carmona , Yueyun Hu

We study a finite range spin glass model in arbitrary dimension, where the intensity of the coupling between spins decays to zero over some distance $\gamma^{-1}$. We prove that, under a positivity condition for the interaction potential,…

Disordered Systems and Neural Networks · Physics 2009-11-10 Silvio Franz , Fabio Lucio Toninelli

We study glassy dynamics using a simulation of three soft Brownian particles confined to a two-dimensional circular region. If the circular region is large, the disks freely rearrange, but rearrangements are rarer for smaller system sizes.…

Soft Condensed Matter · Physics 2016-07-06 Xin Du , Eric R. Weeks

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

Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy…

Disordered Systems and Neural Networks · Physics 2009-11-11 Z. Burda , A. Krzywicki , O. C. Martin , Z. Tabor

The spherical Sherrington-Kirkpatrick model is a spherical mean field model for spin glass. We consider the fluctuations of the free energy at arbitrary non-critical temperature for the 2-spin model with no magnetic field. We show that in…

Probability · Mathematics 2016-09-21 Jinho Baik , Ji Oon Lee

We use heuristic optimization methods in extensive computations to determine with low systematic error ground state configurations of the mean-field $p$-spin glass model with $p=3$. Here, all possible triplets in a system of $N$ Ising spins…

Disordered Systems and Neural Networks · Physics 2025-08-27 Stefan Boettcher , Ginger E. Lau

We study the problem of testing and recovering $k$-clique Ferromagnetic mean shift in the planted Sherrington-Kirkpatrick model (i.e., a type of spin glass model) with $n$ spins. The planted SK model -- a stylized mixture of an uncountable…

Statistics Theory · Mathematics 2024-03-25 Yihan He , Han Liu , Jianqing Fan

The spherical Sherrington-Kirkpatrick (SSK) model and its bipartite analog both exhibit the phenomenon that their free energy fluctuations are asymptotically Gaussian at high temperature but asymptotically Tracy-Widom at low temperature.…

Probability · Mathematics 2023-08-30 Elizabeth Collins-Woodfin , Han Gia Le

One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two…

Condensed Matter · Physics 2007-05-23 E. Brézin , C. De Dominicis

We use real replicas to investigate stability of thermodynamic homogeneity of the free energy of the Sherrington-Kirkpatrick (SK) model of spin glasses. Within the replica trick with the replica symmetric ansatz we show that the averaged…

Disordered Systems and Neural Networks · Physics 2009-11-10 V. Janis , L. Zdeborova

We study properties of the energy minima obtained by quenching equilibrium configurations of the Sherrington-Kirkpatrick (SK) mean field spin glass. We measure the probability distribution of the overlap among quenched configurations and…

Disordered Systems and Neural Networks · Physics 2007-05-23 Barbara Coluzzi , Enzo Marinari , Giorgio Parisi , Heiko Rieger

We compute the probability of positive large deviations of the free energy per spin in mean-field Spin-Glass models. The probability vanishes in the thermodynamic limit as $P(\Delta f) \propto \exp[-N^2 L_2(\Delta f)]$. For the…

Disordered Systems and Neural Networks · Physics 2012-10-31 Giorgio Parisi , Tommaso Rizzo

The topography of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form is investigated numerically using a ``microcanonical'' Monte…

Disordered Systems and Neural Networks · Physics 2007-05-23 Chandan Dasgupta , Oriol T. Valls