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We consider the mean-field classical Heisenberg model and obtain detailed information about the total spin of the system by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain…

Mathematical Physics · Physics 2013-08-23 Kay Kirkpatrick , Elizabeth Meckes

We study the application of a new method for simulating nonlinear dynamics of many-body spin systems using quantum measurement and feedback [Mu\~noz-Arias et al., Phys. Rev. Lett. 124, 110503 (2020)] to a broad class of many-body models…

Quantum Physics · Physics 2020-08-19 Manuel H. Muñoz-Arias , Ivan H. Deutsch , Poul S. Jessen , Pablo M. Poggi

This article considers a class of disordered mean-field combinatorial optimization problems. We focus on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a…

Probability · Mathematics 2024-02-13 Partha S. Dey , Grigory Terlov

We generalize the strategy, we recently introduced to prove the existence of the thermodynamic limit for the Sherrington-Kirkpatrick and p-spin models, to a wider class of mean field spin glass systems, including models with multi-component…

Disordered Systems and Neural Networks · Physics 2007-05-23 Francesco Guerra , Fabio L. Toninelli

A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with $S = \tfrac12$ and external field. For large…

Statistical Mechanics · Physics 2022-02-03 Timo Gräßer , Philip Bleicker , Dag-Björn Hering , Mohsen Yarmohammadi , Götz S. Uhrig

How a system initially at infinite temperature responds when suddenly placed at finite temperatures is a way to check the existence of phase transitions. It has been shown in [R. da Silva, IJMPC 2023] that phase transitions are imprinted in…

A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian, and the calculation of…

Physics Education · Physics 2009-11-11 Bertrand Berche , Alexander Lopez

Motivated by modelling in physics and other disciplines, such as sociology and psychology, we derive the mean field of the general-spin Ising model from the variational principle of the Gibbs free energy. The general-spin Ising model has…

Statistical Mechanics · Physics 2025-09-29 Lourens Waldorp , Tuan Pham , Han L. J. van der Maas

The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a…

Statistical Mechanics · Physics 2009-09-29 Thierry Dauxois , Vito Latora , Andrea Rapisarda , Stefano Ruffo , Alessandro Torcini

We find the free-energy in the thermodynamic limit of a one dimensional XY model associated to a system of N qubits. The coupling among the sigma_i^z is a long range two bodies random interaction. The randomness in the couplings is the…

Mathematical Physics · Physics 2012-01-25 Masha Shcherbina , Brunello Tirozzi

We prove propagation of chaos in the Random field mean-field Ising model, also known ad the Random field Curie-Weiss model. We show that in the paramagnetic phase, i.e.\ in the regime where temperature and distribution of the external field…

Probability · Mathematics 2023-12-05 Matthias Löwe , Zakhar Kabluchko

In the last five decades, mean-field neural-networks have played a crucial role in modelling associative memories and, in particular, the Hopfield model has been extensively studied using tools borrowed from the statistical mechanics of…

Disordered Systems and Neural Networks · Physics 2024-09-17 Elena Agliari , Adriano Barra , Pierluigi Bianco , Alberto Fachechi , Diego Pallara

The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of…

Disordered Systems and Neural Networks · Physics 2012-08-13 H. Chau Nguyen , Johannes Berg

We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of $N$ fully-coupled rotators which…

chao-dyn · Physics 2014-10-13 Vito Latora , Andrea Rapisarda , Stefano Ruffo

We consider the mean field analog of the p-star model for homogeneous random networks, and compare its behaviour with that of the p-star model and its classical mean field approximation in the thermodynamic regime. We show that the…

Statistical Mechanics · Physics 2022-01-26 Gino Biondini , Antonio Moro , Barbara Prinari , Oleg Senkevich

Exploiting the rich phenomenology of periodically-driven many-body systems is notoriously hindered by persistent heating in both the classical and quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir…

Statistical Mechanics · Physics 2022-08-22 Thomas Veness , Kay Brandner

We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and…

Probability · Mathematics 2007-05-23 Christof Kuelske , Arnaud Le Ny , Frank Redig

We prove chaos in temperature for even $p$-spin models which include sufficiently many $p$-spin interaction terms. Our approach is based on a new invariance property for coupled asymptotic Gibbs measures, similar in spirit to the invariance…

Probability · Mathematics 2023-12-13 Dmitry Panchenko

While recent advances have established efficient quantum algorithms for preparing Gibbs states of finite-dimensional systems, comparable complexity results for bosonic and other infinite-dimensional models remain unexplored. We introduce…

Quantum Physics · Physics 2026-04-08 Simon Becker , Cambyse Rouzé , Robert Salzmann

A mean field spherical model with random couplings between pairs, quartets, and possibly higher multiplets of spins is considered. It has the same critical behavior as the Sherrington-Kirkpatrick model. It thus exhibits replica symmetry…

Condensed Matter · Physics 2009-10-22 Th. M. Nieuwenhuizen