Related papers: Gibbs measure for mixed spins and mixed types mode…
We study gradient models for spins taking values in the integers (or an integer lattice), which interact via a general potential depending only on the differences of the spin values at neighboring sites, located on a regular tree with d + 1…
We consider the free boundary condition Gibbs measure of the Potts model on a random tree. We provide an explicit temperature interval below the ferromagnetic transition temperature for which this measure is extremal, improving older bounds…
In this paper we study the boundedness of the $p$-adic quasi Gibbs measures for the Vannimenus model on a Cayley tree of order two.
In this paper we investigate generalized Gibbs measure (GGM) for $p$-adic Hard-Core(HC) model with a countable set of spin values on a Cayley tree of order $k\geq 2$. This model is defined by $p$-adic parameters $\lambda_i$, $i\in \mathbb…
We prove that all Gibbs measures of the $q$-state Potts model on $\mathbb{Z}^2$ are linear combinations of the extremal measures obtained as thermodynamic limits under free or monochromatic boundary conditions. In particular all Gibbs…
We study fragmentation trees of Gibbs type. In the binary case, we identify the most general Gibbs-type fragmentation tree with Aldous' beta-splitting model, which has an extended parameter range $\beta>-2$ with respect to the ${\rm…
We consider fertile three-state Hard-Core (HC) models with the activity parameter $\lambda>0$ on a Cayley tree. It is known that there exist four types of such models: wrench, wand, hinge, and pipe. These models arise as simple examples of…
For the solid-on-solid (SOS) model with spin values from the set of all integers on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (which is an infinite-dimensional vector-valued function…
In this paper adapting to $p$-adic case some methods of real valued Gibbs measures on Cayley trees we construct several $p$-adic distributions on the set $\mathbb{Z}_p$ of $p$-adic integers. Moreover, we give conditions under which these…
In the present paper, we introduce a new kind of $p$-adic measures for $q+1$-state Potts model, called {\it $p$-adic quasi Gibbs measure}. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we…
We consider the soft-core Widom-Rowlinson model for particles with spins and holes, on a Cayley tree of order $d$ (which has $d + 1$ nearest neighbours), depending on repulsion strength $\beta$ between particles of different signs and on an…
Using topological summaries of gene trees as a basis for species tree inference is a promising approach to obtain acceptable speed on genomic-scale datasets, and to avoid some undesirable modeling assumptions. Here we study the…
We consider Potts model, with competing interactions and countable spin values $\Phi=\{0,1,\dots \}$ on a Cayley tree of order three. We study periodic ground states for this model.
In this present paper, the recurrence equations of an Ising model with three coupling constants on a third-order Cayley tree are obtained. Paramagnetic and ferromagnetic phases associated with the Ising model are characterized. Types of…
We consider both Hard-Core and Soft-Core Widom-Rowlinson models with spin values $-1,0,1$ on a Cayley tree of order $k\geq 2$ and we are interested in the Gibbs measures of the models. The models depend on 3 parameters: the order $k$ of the…
Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…
Nonparametric Bayesian approaches to clustering, information retrieval, language modeling and object recognition have recently shown great promise as a new paradigm for unsupervised data analysis. Most contributions have focused on the…
We consider the Potts model with two-step interactions and spin values 1,2,3,4 on a Cayley tree. We describe periodic ground states and verify the Peierls condition for the model.
We provide an existence theory for gradient Gibbs measures for Z-valued spin models on regular trees which are not invariant under translations of the tree, assuming only summability of the transfer operator. The gradient states we obtain…
In this paper we analytically study the recurrence equations of an Ising model with three competing interactions on a Cayley tree of order three. We exactly describe paramagnetic and ferromagnetic phases of the Ising model. We obtain some…