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We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an…

Mathematical Physics · Physics 2018-09-26 Rodrigo Bissacot , Eric Ossami Endo , Aernout C. D. van Enter , Arnaud Le Ny

We study the Gibbs measure of the nonhierarchical versions of the Generalized Random Energy Models introduced in previous work. We prove that the ultrametricity holds only provided some nondegeneracy conditions on the hamiltonian are met.

Probability · Mathematics 2008-11-17 Erwin Bolthausen , Nicola Kistler

In a general class of one and two dimensional Hubbard models, we prove upper bounds for the two-point correlation functions at finite temperatures for electrons, for electron pairs, and for spins. The upper bounds decay exponentially in one…

Statistical Mechanics · Physics 2009-10-30 Tohru Koma , Hal Tasaki

For a family of integer-valued height functions defined over the faces of planar graphs, we establish a relation between the probability of connection by level sets and the spin-spin correlations of the dual $O(2)$ symmetric spin models…

Probability · Mathematics 2022-05-30 Michael Aizenman , Matan Harel , Ron Peled , Jacob Shapiro

We review some recent developments in the study of Gibbs and non-Gibbs properties of transformed n-vector lattice and mean-field models under various transformations. Also, some new results for the loss and recovery of the Gibbs property of…

Mathematical Physics · Physics 2008-12-10 A. C. D. van Enter , C. Kuelske , A. A. Opoku , W. M. Ruszel

We generalise disagreement percolation to Gibbs point processes of balls with varying radii. This allows to establish the uniqueness of the Gibbs measure and exponential decay of pair correlations in the low activity regime by comparison…

Probability · Mathematics 2019-04-24 Christoph Hofer-Temmel , Pierre Houdebert

We consider the Curie-Weiss model at a given initial temperature in vanishing external field evolving under a Glauber spin-flip dynamics corresponding to a possibly different temperature. We study the limiting conditional probabilities and…

Mathematical Physics · Physics 2015-05-18 Victor Ermolaev , Christof Kuelske

Dynamics under which a system of Ising spins relaxes to a stationary state with Bolzmann-Gibbs measure and which do not fulfil the condition of detailed balance are irreversible and asymmetric. We revisit the problem of the determination of…

Statistical Mechanics · Physics 2015-06-15 Claude Godreche

The thermal equilibrium properties of physical systems can be described using Gibbs states. It is therefore of great interest to know when such states allow for an easy description. In particular, this is the case if correlations between…

Quantum Physics · Physics 2022-03-01 Andreas Bluhm , Ángela Capel , Antonio Pérez-Hernández

The infinite-volume limit behavior of the 2d Ising model under possibly strong random boundary conditions is studied. The model exhibits chaotic size-dependence at low temperatures and we prove that the `+' and `-' phases are the only…

Mathematical Physics · Physics 2015-06-26 A. C. D. van Enter , K. Netocny , H. G. Schaap

This paper deals with the problem of perfect sampling from a Gibbs measure with infinite range interactions. We present some sufficient conditions for the extinction of processes which are like supermartingales when large values are taken.…

Probability · Mathematics 2015-05-28 Emilio De Santis , Andrea Lissandrelli

Gibbs measures are the main object of study in equilibrium statistical mechanics, and are used in many other contexts, including dynamical systems and ergodic theory, and spatial statistics. However, in a large number of natural instances…

Mathematical Physics · Physics 2012-04-27 A. C. D. van Enter

We consider a system of real-valued spins interacting with each other through a mean-field Hamiltonian that depends on the empirical magnetization of the spins via a general potential. The system is subjected to a stochastic dynamics where…

Probability · Mathematics 2014-10-29 Frank den Hollander , Frank Redig , Willem van Zuijlen

In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential…

High Energy Physics - Theory · Physics 2015-09-30 Roberto Bonezzi , Per Sundell , Alexander Torres-Gomez

The previously developed n-vicinity method allows us to calculate accurately critical values of inverse temperatures for Ising models with short-range interaction. We generalize the method to the case of long-range interactions in spin…

Statistical Mechanics · Physics 2020-12-15 Inna Kaganowa , Boris Kryzhanovsky , Leonid Litinskii

On the space of Ising configurations on the 2-d square lattice, we consider a family of non Gibbsian measures introduced by using a pair Hamiltonian, depending on an additional inertial parameter $q$. These measures are related to the usual…

We continue our study of Gibbs-non-Gibbs dynamical transitions. In the present paper we consider a system of Ising spins on a large discrete torus with a Kac-type interaction subject to an independent spin-flip dynamics…

Mathematical Physics · Physics 2015-06-17 Roberto Fernández , Frank den Hollander , Julián Martínez

Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. We introduce a geometric description of the spin…

Mathematical Physics · Physics 2011-11-09 M. Cassandro , P. A. Ferrari , I. Merola , E. Presutti

We study measures on the configuration spaces of two type particles. Gibbs measures on the such spaces are described. Main properties of corresponding relative energies densities and correlation functions are considered. In particular, we…

Mathematical Physics · Physics 2015-01-27 D. L. Finkelshtein

Monte Carlo data of the two-dimensional Ising spin glass with bimodal interactions are presented with the aim of understanding the low-temperature physics of the model. An analysis of the specific heat, spin-glass susceptibility,…

Disordered Systems and Neural Networks · Physics 2007-05-23 Helmut G. Katzgraber , Lik Wee Lee , I. A. Campbell