Related papers: Gibbs States on Random Configurations
One proves the equivalence of a Gibbs measure and a Gibbs conformal measure for a dynamical system (G,X) when G is a countably infinite discrete group acting expansively on a compact ultrametric space X. As an application one proves for any…
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…
The article deals with spin s=1 magnets. The symmetry conditions for normal and degenerate equilibrium states are defined and types of magnetic ordering found out. For each type of symmetry breaking the structure of source in the Gibbs…
We formulate and prove a very general relative version of the Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of configuration spaces over a finite alphabet such that for every absolutely summable relative…
Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to…
We consider statistical mechanics models of continuous spins in a disordered environment. These models have a natural interpretation as effective interface models. It is well known that without disorder there are no interface Gibbs measures…
We analyze the physical meaning of a possible experiment aimed at the simultaneous measurement of two non-commuting spin components. We demonstrate that switching of a strong spin-orbit interaction, e.g., in a solid state or a cold-atom…
The notion of Gibbs Measure is used by many researchers of the communities of Mathematical Physics, Probability, Thermodynamic Formalism, Symbolic Dynamics, and others. A natural question is when these several different notions of Gibbs…
We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each partricle is characterised by its position $x\in \mathbb{R}^{d}$ and internal parameter…
We present a modified Gibbs sampler for general state spaces. We establish that this modification can lead to substantial gains in statistical efficiency while maintaining the overall quality of convergence. We illustrate our results in two…
For $m$ number of bosons, carrying spin ($S$=1) degree of freedom, in $\Omega$ number of single particle orbitals, each triply degenerate, we introduce and analyze embedded Gaussian orthogonal ensemble of random matrices generated by random…
This paper deals with stationary Gibbsian point processes on the plane with an interaction that depends on the tiles of the Delaunay triangulation of points via a bounded triangle potential. It is shown that the class of these Gibbs…
We study a classical integrable (Neumann) model describing the motion of a particle on the sphere, subject to harmonic forces. We tackle the problem in the infinite dimensional limit by introducing a soft version in which the spherical…
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…
In generic classical and quantum many-body systems, where typically energy and particle number are the only conserved quantities, stationary states are described by thermal equilibrium. In contrast, integrable systems showcase an infinite…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of…
Can the joint measures of quenched disordered lattice spin models (with finite range) on the product of spin-space and disorder-space be represented as (suitably generalized) Gibbs measures of an ``annealed system''? - We prove that there…
A key insight from statistical physics about spin systems on random graphs is the central role played by Gibbs measures on trees. We determine the local weak limit of the hardcore model on random regular graphs asymptotically until just…
We are interested in the study of Gibbs and equilbrium probabilities on the lattice $\mathbb{R}^{\mathbb{N}}$. Consider the unilateral full-shift defined on the non-compact set $\mathbb{R}^{\mathbb{N}}$ and an $\alpha$-H\"older continuous…