Related papers: Gibbs measure for mixed spins and mixed types mode…

For the $q-$state Potts model new order parameters projecting on a group of spins instead of a single spin are introduced. On a Cayley tree this allows the physical interpretation of the Potts model at noninteger values q of the number of…

Two-sort species yield differential equations for functional digraphs of Cayley permutations. From these we obtain an explicit formula for fixed-point-free Cayley permutations and prove that their proportion tends to $1/e$, as for…

In the present paper, by conducting research on the dynamics of the $p$-adic generalized Ising mapping corresponding to renormalization group associated with the $p$-adic Ising-Vannemenus model on a Cayley tree, we have determined the…

The distribution $g_{cl}$ of a Gibbs cluster point process in $X=\mathbb{R}^{d}$ (with i.i.d. random clusters attached to points of a Gibbs configuration with distribution $g$) is studied via the projection of an auxiliary Gibbs measure…

Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems…

This paper is devoted to the study of Gibbs u-states for the geodesic flow tangent to a foliation with negatively curved leaves. On the one hand we give sufficient conditions for the existence of transverse invariant measures. In particular…

In this paper we'll give a connection between four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) of models with uncountable (i.e. $[0,1]$) set of spin values on the Cayley tree of order…

In the study of Ising models on large locally tree-like graphs, in both rigorous and non-rigorous methods one is often led to understanding the so-called belief propagation distributional recursions and its fixed points. We prove that there…

We present, for the Ising model on the Cayley tree, some explicit formulae of the free energies (and entropies) according to boundary conditions (b.c.). They include translation-invariant, periodic, Dobrushin-like b.c., as well as those…

We investigate the phase diagram of a spin--1 Ising spin-glass model on a Cayley tree. According to early work of Thompson and collaborators, this problem can be formulated in terms of a set of nonlinear discrete recursion relations along…

Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…

Gibbs partitions of the integers generated by stable subordinators of index $\alpha\in(0,1)$ form remarkable classes of random partitions where in principle much is known about their properties, including practically effortless obtainment…

We study the nonequilibrium properties of directed Ising models with non conserved dynamics, in which each spin is influenced by only a subset of its nearest neighbours. We treat the following models: (i) the one-dimensional chain; (ii) the…

The Gibbs Mixing Paradox is a conceptual touchstone for understanding mixtures in statistical mechanics. While debates over the theoretical subtleties of particle distinguishability continue to this day, we seek to extend the discussion in…

Some results on the two-point function and on the analytic structure of the momenta of the effective fugacity at the origin for a class of diluted ferromagnetic Ising models on the Cayley tree are presented.

In this paper we define a variant of the Ising model in which spins are replaced with permutations. The energy between two spins is a function of the relative disorder of one spin, a permutation, to the other. This model is motivated by a…

In this paper, correlation inequalities which have been considered on Ising model are extended to q-Potts model. It is considered on generalized Potts model with interaction of any number of spins. We replace the set of spin values…

We prove a new formula for the generating function of multitype Cayley trees counted according to their degree distribution. Using this formula we recover and extend several enumerative results about trees. In particular, we extend some…

This work is concerned with the theory of Graphical Representation for the Ising and Potts Models over general lattices with non-translation invariant external field. We explicitly describe in terms of the Random Cluster Representation the…

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…