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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

Classical Markov Chain Monte Carlo methods have been essential for simulating statistical physical systems and have proven well applicable to other systems with many degrees of freedom. Motivated by the statistical physics origins, Chen,…

Quantum Physics · Physics 2026-01-26 András Gilyén , Chi-Fang Chen , Joao F. Doriguello , Michael J. Kastoryano

A brief survey of the theoretical, numerical and experimental studies of the random field Ising model during last three decades is given. Nature of the phase transition in the three-dimensional RFIM with Gaussian random fields is discussed.…

Disordered Systems and Neural Networks · Physics 2009-11-13 Victor Dotsenko

We develop a mean-field theory for random quantum spin systems using the spin coherent state path integral representation. After the model is reduced to the mean field one-body Hamiltonian, the integral is analyzed with the aid of several…

Disordered Systems and Neural Networks · Physics 2007-11-20 Kazutaka Takahashi

We consider the random field M(t)=\sup_{n\geq 1}\big\{-\log A_{n}+X_{n}(t)\big\}\,,\qquad t\in T\, for a set $T\subset \mathbb{R}^{m}$, where $(X_{n})$ is an iid sequence of centered Gaussian random fields on $T$ and $0<A_{1}<A_{2}<\cdots $…

Probability · Mathematics 2018-03-28 Zhipeng Liu , Jose H. Blanchet , A. B. Dieker , Thomas Mikosch

We consider the homogeneous mean-field Bose gas at temperatures proportional to the critical temperature of its Bose-Einstein condensation phase transition. We prove a trace norm approximation for the grand canonical Gibbs state in terms of…

Mathematical Physics · Physics 2025-08-25 Andreas Deuchert , Phan Thành Nam , Marcin Napiórkowski

We analyze the statics for pure $p$-spin spherical spin glass models with $p\geq3$, at low enough temperature. With $F_{N,\beta}$ denoting the free energy, we compute the second order (logarithmic) term of $NF_{N,\beta}$ and prove that, for…

Probability · Mathematics 2017-10-11 Eliran Subag

We study statistical characterization of the many-body states in exactly solvable models with internal degrees of freedom. The models under consideration include the isotropic and anisotropic Heisenberg spin chain, the Hubbard chain, and a…

Condensed Matter · Physics 2009-10-28 Y. Hatsugai , M. Kohmoto , T. Koma , Y. -S. Wu , Comments

In the context of disordered systems with quenched Hamiltonians I address the problem of characterizing rare samples where the thermal average of a specific observable has a value different from the typical one. These rare samples can be…

Disordered Systems and Neural Networks · Physics 2014-05-05 Tommaso Rizzo

We combine the single site dynamical mean field theory (DMFT) with the non-local GW method. This is done fully self-consistently and we apply our formalism to a one-band Hubbard model. Eventually at self-consistency the full self-energy and…

Strongly Correlated Electrons · Physics 2007-05-23 K. Karlsson

This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…

Dynamical Systems · Mathematics 2017-02-06 Volker Mayer , Mariusz Urbanski

Aim of this work is not trying to explore a macroscopic behavior of some recent model in statistical mechanics but showing how some recent techniques developed within the framework of spin glasses do work on simpler model, focusing on the…

Disordered Systems and Neural Networks · Physics 2009-11-13 Adriano Barra

We propose a new method of solving a class of mean-field (MF) models, which is based on the Maximum Entropy (MaxEnt) principle with additional constraints included. Next, we show equivalence of our method when applied to the Gutzwiller…

Strongly Correlated Electrons · Physics 2011-05-19 Jakub Jȩdrak , Jan Kaczmarczyk , Jozef Spałek

Francesco Guerra and Fabio Toninelli have developped a very powerful technique to study the high temperature behaviour of the Sherrington-Kirkpatrick mean field spin glass model. They show that this model is asymptoticaly comparable to a…

Probability · Mathematics 2007-05-23 Philippe Carmona

Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of $N$ globally coupled particles moving on…

Statistical Mechanics · Physics 2012-01-09 Pierre de Buyl , David Mukamel , Stefano Ruffo

We study equilibrium states of an infinite system of interacting particles in a Euclidean space. The particles bear `unbounded' spins with a given symmetric a priori distribution. The interaction between the particles is pairwise and splits…

Mathematical Physics · Physics 2017-04-26 Diana Conache , Alexei Daletskii , Yuri Kondratiev , Tanja Pasurek

We present a numerical study of the zero-temperature response of the Gaussian random-field Ising model (RFIM) to a slowly varying external field, allowing the system to be trapped in microscopic configurations that are not fully metastable.…

Disordered Systems and Neural Networks · Physics 2009-07-17 F. Salvat-Pujol , E. Vives , M. L. Rosinberg

It is known that a linear hamiltonian system has too many invariant measures, thus the problem of convergence to Gibbs measure has no sense. We consider linear hamiltonian systems of arbitrary finite dimension and prove that, under the…

Mathematical Physics · Physics 2013-02-21 A. A. Lykov , V. A. Malyshev

In the present paper we study some correlation effects in a generalized Hubbard model with correlated hopping within low-temperature region using a generalized mean-field approximation. It is shown that in a series of cases the model leads…

Strongly Correlated Electrons · Physics 2009-10-31 L. Didukh , V. Hankevych , Yu. Skorenkyy

The Hamiltonian of mean force is a widely used concept to describe the modification of the usual canonical Gibbs state for a quantum system whose coupling strength with the thermal bath is non-negligible. Here we perturbatively derive…

Quantum Physics · Physics 2022-10-26 Grigorii Timofeev , Anton Trushechkin