Results 11 - 20 of 236

Bijections for Cayley trees, spanning trees, and their q-analogues

by Jeffrey B. Remmel - Journal of Combinatorial Theory , 1986
"... We construct a family of extremely simple bijections that yield Cayley’s famous formula for counting trees. The weight preserving properties of these bijections fur-nish a number of multivariate generating functions for weighted Cayley trees. Essentially the same idea is used to derive bijective pro ..."
Abstract - Cited by 24 (5 self) - Add to MetaCart
We construct a family of extremely simple bijections that yield Cayley’s famous formula for counting trees. The weight preserving properties of these bijections fur-nish a number of multivariate generating functions for weighted Cayley trees. Essentially the same idea is used to derive bijective

Susceptibility and Correlation Function of the Ising Model on the Cayley Tree

by Tohru Morita, Tsuyoshi Horiguchi , 1974
"... The exact expressions are given for the correlation functions and the isothermal sus-ceptibility of the Ising model on the finite Cayley tree under zero external field, and for those quantities in the thermodynamic limit. Matsuda's conclusions, the absence.of the spontaneous magnetization and t ..."
Abstract - Add to MetaCart
The exact expressions are given for the correlation functions and the isothermal sus-ceptibility of the Ising model on the finite Cayley tree under zero external field, and for those quantities in the thermodynamic limit. Matsuda's conclusions, the absence.of the spontaneous magnetization

A Contour Method on Cayley tree 1

by U. A. Rozikov , 2006
"... Abstract: We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of s diffe ..."
Abstract - Add to MetaCart
Abstract: We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence

ON PERIODIC WAVE FUNCTIONS OF SCHRÖDINGER OPERATORS ON CAYLEY TREES

by Fumio Hiroshima, Utkir Rozikov
"... Abstract. In the paper we define periodic wave functions for a (discrete) Schrödinger operator on a Cayley tree. This periodicity depends on a subgroup of a group repre-sentation of the Cayley tree. For any subgroup of finite index we give a criterion for eigenvalues of the Schrödinger operator un ..."
Abstract - Add to MetaCart
Abstract. In the paper we define periodic wave functions for a (discrete) Schrödinger operator on a Cayley tree. This periodicity depends on a subgroup of a group repre-sentation of the Cayley tree. For any subgroup of finite index we give a criterion for eigenvalues of the Schrödinger operator

PACEMAKERS IN A CAYLEY TREE OF KURAMOTO OSCILLATORS

by Pablo M. Gleiser, Centro Atómico Bariloche, Luce Prignano, Conrad J. Pérez-vicente, Albert Díaz-guilera , 2010
"... In this work, we study a system of Kuramoto oscillators with identical frequencies in a Cayley tree. Heterogeneity in the frequency distribution is introduced in the root of the tree, allowing for analytical calculations of the phase evolution. In this work, we study a system of Kuramoto oscillators ..."
Abstract - Add to MetaCart
In this work, we study a system of Kuramoto oscillators with identical frequencies in a Cayley tree. Heterogeneity in the frequency distribution is introduced in the root of the tree, allowing for analytical calculations of the phase evolution. In this work, we study a system of Kuramoto

On periodic p-harmonic functions on Cayley tree.

by U. A. Rozikov, F. T. Ishankulov , 803
"... Abstract: We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index p-harmonic function is a constant. For some normal subgroups of infinite index we describe a class of (non-constant) periodic p-harmonic functions. If p = 2, the p-h ..."
Abstract - Cited by 2 (2 self) - Add to MetaCart
Abstract: We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index p-harmonic function is a constant. For some normal subgroups of infinite index we describe a class of (non-constant) periodic p-harmonic functions. If p = 2, the p

ON FREE ENERGIES OF THE ISING MODEL ON THE CAYLEY TREE

by D. Gandolfo, M. M. Rakhmatullaev, U. A. Rozikov, J. Ruiz
"... Abstract. 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 in-clude translation-invariant, periodic, Dobrushin-like b.c., as well as those corresponding to (recently discovered) weakly period ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
Abstract. 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 in-clude translation-invariant, periodic, Dobrushin-like b.c., as well as those corresponding to (recently discovered) weakly

Rigidity of the critical phases on a Cayley tree

by P. Bleher, J. Ruiz, R. H. Schonmann, S. Shlosman, V. Zagrebnov - Moscow Mathematical Journal , 2001
"... We discuss statistical mechanics on non-amenable graphs, and we study the features of the phase transition, which are due to non-amenability. For the Ising model on the usual lattice it is known that uctuations of magnetization are much less likely in the states with non-zero magnetic eld than in th ..."
Abstract - Cited by 13 (0 self) - Add to MetaCart
in the pure states with zero eld. We show that on the Cayley tree the corresponding uctuations have the same order. Key words and phrases: tree, non-amenable graph, Ising model, large deviations, droplet. 1 Introduction and statement of results This paper is a result of our attempt to understand the nature

New phase transitions of the Ising model on Cayley trees

by D. Gandolfo, F. H. Haydarov, U. A. Rozikov, J. Ruiz - J. Stat. Phys , 2013
"... Abstract. 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 the number of Gibbs states as well as by a drastic ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
Abstract. 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 the number of Gibbs states as well as by a drastic

ON FOUR STATE HARD CORE MODELS ON THE CAYLEY TREE

by D. Gandolfo, U. A. Rozikov, J. Ruiz
"... Abstract. We consider a nearest-neighbor four state hard-core (HC) model on the homogeneous Cayley tree of order k. The Hamiltonian of the model is considered on a set of “admissible ” configurations. Admissibility is specified through a graph with four vertices. We first exhibit conditions (on the ..."
Abstract - Add to MetaCart
Abstract. We consider a nearest-neighbor four state hard-core (HC) model on the homogeneous Cayley tree of order k. The Hamiltonian of the model is considered on a set of “admissible ” configurations. Admissibility is specified through a graph with four vertices. We first exhibit conditions (on
Results 11 - 20 of 236