English
Related papers

Related papers: Universal structures in some mean field spin glass…

200 papers

We study the quenched complexity in spin-glass mean-field models satisfying the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study, consistent with recent numerical results, allows, in principle, to conjecture the absence of…

Disordered Systems and Neural Networks · Physics 2009-11-10 A. Crisanti , L. Leuzzi , G. Parisi , T. Rizzo

We investigate the structure of Parisi measures, the functional order parameters of mixed p-spin models in mean field spin glasses. In the absence of external field, we prove that a Parisi measure satisfies the following properties. First,…

Probability · Mathematics 2013-03-18 Antonio Auffinger , Wei-Kuo Chen

We present results from Monte Carlo simulations to test for ultrametricity and clustering properties in spin-glass models. By using a one-dimensional Ising spin glass with random power-law interactions where the universality class of the…

Disordered Systems and Neural Networks · Physics 2009-01-26 Helmut G. Katzgraber , Alexander K. Hartmann

We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this…

Disordered Systems and Neural Networks · Physics 2026-05-05 Silvio Franz , Giorgio Parisi , Federico Ricci-Tersenghi

We study mean-field spin glass models with general vector spins and convex covariance function. For those models, it is known that the limit of the free energy can be written as the supremum of a functional, this is the celebrated Parisi…

Probability · Mathematics 2024-10-14 Victor Issa

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

We study the free energy of mean-field multi-species spin glasses with convex covariance function. For such models with $D$ species, the Parisi formula is known to be valid, and expresses the limit free energy as a supremum over monotone…

Probability · Mathematics 2025-08-11 Hong-Bin Chen , Victor Issa , Jean-Christophe Mourrat

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…

Mathematical Physics · Physics 2017-06-19 J. P. Keating , N. Linden , H. J. Wells

We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model and the one without an external field. We…

Disordered Systems and Neural Networks · Physics 2021-05-26 Jinho Baik , Elizabeth Collins-Woodfin , Pierre Le Doussal , Hao Wu

We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic…

Probability · Mathematics 2017-03-13 Antonio Auffinger , Wei-Kuo Chen

We study the L\'evy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses…

Disordered Systems and Neural Networks · Physics 2010-01-29 I. Neri , F. L. Metz , D. Bollé

We investigate the classical Renyi entropy S_n and the associated mutual information I_n in the Sherrington-Kirkpatrick (S-K) model, which is the paradigm model of mean-field spin glasses. Using classical Monte Carlo simulations and…

Statistical Mechanics · Physics 2016-04-26 Vincenzo Alba , Stephen Inglis , Lode Pollet

We prove a Parisi formula for the limiting free energy of multi-species spherical spin glasses with mixed $p$-spin interactions. The upper bound involves a Guerra-style interpolation and requires a convexity assumption on the model's…

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

The synthetic spin-orbit coupled quantum gases is widely studied both experimentally and theoretically in recent years. As previous studies show, this modification of single-body dispersion will in general couple different partial waves and…

Quantum Gases · Physics 2018-04-25 Pengfei Zhang , Ning Sun

We introduce some applications of Stein's method in the high temperature analysis of spin glasses. Stein's method allows the direct analysis of the Gibbs measure without having to create a cavity. Another advantage is that it gives limit…

Probability · Mathematics 2009-08-02 Sourav Chatterjee

The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via…

Disordered Systems and Neural Networks · Physics 2013-03-27 V. Janis , A. Kauch , A. Klic

The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking…

Disordered Systems and Neural Networks · Physics 2007-05-23 D. S. Dean , F. Ritort

We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function $q(x)$ is computed at high orders in powers of $\tau=T_c-T$ and $H$. We find that none of…

Disordered Systems and Neural Networks · Physics 2009-11-10 A. Crisanti , T. Rizzo , T. Temesvari

The state space for the $N$-spin mean field (SK) spin glass--nominally an $N$-cube--is embedded in a low dimensional continuous space in such a way that metastable and stable phases can easily be discerned, a concept of nearness of…

Statistical Mechanics · Physics 2007-11-08 L. S. Schulman

We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for…

Condensed Matter · Physics 2009-01-23 Bernd A. Berg , Wolfhard Janke