Related papers: Gradient Gibbs measures for the SOS model with int…
We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schroedinger equations on the disc of the plane $\R^2$. We also prove an estimate giving some intuition to what may happen in 3…
We consider the incompressible and stationary Stokes equations on an infinite two-dimensional wedge with non-scaling invariant Navier-slip boundary conditions. We prove well-posedness and higher regularity of the Stokes problem in a certain…
In this paper we develop a notion of Gibbs measure for the geodesic flow tangent to a foliated bundle over a compact and negatively curved basis. We also develop a notion of $F$-harmonic measure and prove that there exists a natural…
For the Potts model on the Cayley tree, some explicit formulae of the free energies and entropies (according to vector-valued boundary conditions (BCs)) are obtained. They include translation-invariant, periodic, Dobrushin-like BCs, as well…
In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We…
In this paper we consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid…
We study the Ising model on a Cayley tree. A wide class of new Gibbs states is exhibited.
We show that the nearest neighbors Ising model on the Cayley tree exhibits new temperature driven phase transitions. These transitions holds at various inverse temperatures different from the critical one. They are depicted by a change in…
We consider general classes of gradient models on regular trees with values in a countable Abelian group $S$ such as $\mathbb{Z}$ or $\mathbb{Z}_q$, in regimes of strong coupling (or low temperature). This includes unbounded spin models…
In this paper we consider a model on a Cayley tree which has a finite radius of interactions, the model was first considered by Rozikov. We describe a set of periodic ground states of the model.
We consider the ferromagnetic Ising model on the Cayley tree and we investigate the decomposition of the free state into extremal states below the spin glass temperature. We show that this decomposition has uncountably many components. The…
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…
Cayley's formula states that there are $n^{n-2}$ spanning trees in the complete graph on $n$ vertices; it has been proved in more than a dozen different ways over its 150 year history. The complete graphs are a special case of threshold…
For all integers $k\geq 3$, we give an $O(n^4)$ time algorithm for the problem whose instance is a graph $G$ of girth at least $k$ together with $k$ vertices and whose question is "Does $G$ contains an induced subgraph containing the $k$…
Following [1] we study a QCD-like gauge theory using a non-supersymmetric setup in type IIB string theory. The setup includes an $O3$ plane and $N$ D3 anti-branes and it realises a $USp(2N)$ 'electric' gauge theory with four "quarks" in the…
In this paper we consider translation-invariant Gibbs measures for the Blum-Kapel model on a Cayley tree of order k. An approximate critical temperature T_{cr} is found such that for T\geq T_{cr} there exists a unique translation-invariant…
Standard SUSY-GUTs such as those based on $SU(5)$ or $SO(10)$ lead to predictions for the values of $\alpha _s$ and $sin^2\theta _W$ in amazing agreement with experiment. In this article we investigate how these models may be obtained from…
We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for a class of external fields, asymptotically approaching a…
We present the first known pivot Gray code for spanning trees of complete graphs, listing all spanning trees such that consecutive trees differ by pivoting a single edge around a vertex. This pivot Gray code thus addresses an open problem…
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…