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Related papers: A simple approach to chaos for $p$-spin models

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We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show…

Dynamics of spin-glasses subjected to slow continuous changes of working enviroment such as slow changes of temperature or interaction bonds are studied based on scaling arguments and numerical simulations of continuous bond changes. Such…

Disordered Systems and Neural Networks · Physics 2009-11-10 Hajime Yoshino , Petra E. Jonsson

Spin glasses have competing interactions that lead to a rough energy landscape which is highly susceptible to small perturbations. These chaotic effects strongly affect numerical simulations and, as such, gaining a deeper understanding of…

Disordered Systems and Neural Networks · Physics 2016-06-14 Wenlong Wang , Jonathan Machta , Helmut G. Katzgraber

We prove that the Sherrington-Kirkpatrick model of spin glasses is chaotic under small perturbations of the couplings at any temperature in the absence of an external field. The result is proved for two kinds of perturbations: (a)…

Probability · Mathematics 2009-11-24 Sourav Chatterjee

We show that the thermodynamic limit of the ground state energy in the mixed p-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.

Probability · Mathematics 2016-06-29 Antonio Auffinger , Wei-Kuo Chen

We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the two models, such as, temperature, disorder,…

Probability · Mathematics 2013-11-12 Wei-Kuo Chen

We sketch a new framework for the analysis of disordered systems, in particular mean field spin glasses, which is variational in nature and within the formalism of classical thermodynamics. For concreteness, only the Sherrington-Kirkpatrick…

Probability · Mathematics 2019-02-26 Goetz Kersting , Nicola Kistler , Adrien Schertzer , Marius A. Schmidt

This review presents various aspects of a mean-field spin glass model known as the p-spin spherical spin glass model, which has raised a lot of interest in the study of spin glasses, and also for its possible links with a mean-field theory…

Disordered Systems and Neural Networks · Physics 2008-02-03 A. Barrat

In a recent breakthrough [arXiv:2301.04112], Chatterjee proved site disorder chaos in the Edwards-Anderson (EA) short-range spin glass model utilizing the Hermite spectral method. In this paper, we demonstrate the further usefulness of this…

Probability · Mathematics 2025-04-09 Wei-Kuo Chen , Heejune Kim , Arnab Sen

We consider whether it is possible to find ground states of frustrated spin systems by solving them locally. Using spin glass physics and Imry-Ma arguments in addition to numerical benchmarks we quantify the power of such local solution…

Disordered Systems and Neural Networks · Physics 2015-01-12 Ilia Zintchenko , Matthew B. Hastings , Matthias Troyer

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 a large-$N$ bosonic quantum mechanical sigma-model with a spherical target space subject to disordered interactions, more colloquially known as the $p$-spin spherical model. Replica symmetry is broken at low temperatures and for…

High Energy Physics - Theory · Physics 2021-11-04 Tarek Anous , Felix M. Haehl

This is a short review about recent methods and results, mostly for mean field spin glasses, based on interpolation and comparison schemes. In particular, the Parisi spontaneous replica symmetry breaking phenomenon is described in the frame…

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

A disordered spin glass model where both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system…

Disordered Systems and Neural Networks · Physics 2009-10-31 M. Pasquini , M. Serva

In an effort to understand the glass transition, the kinetics of a spin model with frustration but no quenched randomness has been analyzed. The phenomenology of the spin model is remarkably similiar to that of structural glasses. Analysis…

Statistical Mechanics · Physics 2009-10-31 Bulbul Chakraborty , Lei Gu , Hui Yin

When applied to dynamical systems, both classical and quantum, time periodic modulations can produce complex non-equilibrium states which are often termed 'chaotic`. Being well understood within the unitary Hamiltonian framework, this…

Quantum Physics · Physics 2024-06-19 I. I. Yusipov , S. V. Denisov , M. V. Ivanchenko

We numerically study quantum chaos properties of long-range XXZ dipolar Hamiltonian spin systems. Two geometries are considered: (i) an open chain with 19 spins, (ii) a face-centered cubic lattice with 14 spins. Energy level-spacing…

Quantum Physics · Physics 2017-11-07 Dhrubo Jyoti

The nature of static chaos in Ising spin glasses is studied. For the problem of chaos with magnetic field, scaling relations in the case of the SK model and short-range models are presented. Our results also suggest that if there is de…

Condensed Matter · Physics 2007-05-23 Felix Ritort

The onset of chaos in one-dimensional spinning particle models derived from pseudoclassical mechanical hamiltonians with a bosonic Duffing potential is examined. Using the Melnikov method, we indicate the presence of homoclinic…

Chaotic Dynamics · Physics 2009-11-07 H. T. Cho , J. -K. Kao

Spin glasses occupy a unique place in condensed matter: they freeze collectively while remaining struc-turally disordered, and they exhibit slow, history-dependent dynamics that reflect an exceptionally rug-ged free-energy landscape. This…

Disordered Systems and Neural Networks · Physics 2025-12-25 Naeimeh Tahriri , Vahid Mahdikhah , Jahanfar Abouie , Daryoosh Vashaee