Results 11  20
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236
Bijections for Cayley trees, spanning trees, and their qanalogues
 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 furnish a number of multivariate generating functions for weighted Cayley trees. Essentially the same idea is used to derive bijective pro ..."
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Cited by 24 (5 self)
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We construct a family of extremely simple bijections that yield Cayley’s famous formula for counting trees. The weight preserving properties of these bijections furnish 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
, 1974
"... The exact expressions are given for the correlation functions and the isothermal susceptibility 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 ..."
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The exact expressions are given for the correlation functions and the isothermal susceptibility 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
, 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 ..."
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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
"... 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 representation of the Cayley tree. For any subgroup of finite index we give a criterion for eigenvalues of the Schrödinger operator un ..."
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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 representation 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
, 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 ..."
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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 pharmonic functions on Cayley tree.
, 803
"... Abstract: We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index pharmonic function is a constant. For some normal subgroups of infinite index we describe a class of (nonconstant) periodic pharmonic functions. If p = 2, the ph ..."
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Cited by 2 (2 self)
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Abstract: We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index pharmonic function is a constant. For some normal subgroups of infinite index we describe a class of (nonconstant) periodic pharmonic functions. If p = 2, the p
ON FREE ENERGIES OF THE ISING MODEL ON THE CAYLEY TREE
"... 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 include translationinvariant, periodic, Dobrushinlike b.c., as well as those corresponding to (recently discovered) weakly period ..."
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Cited by 1 (1 self)
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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 include translationinvariant, periodic, Dobrushinlike b.c., as well as those corresponding to (recently discovered) weakly
Rigidity of the critical phases on a Cayley tree
 Moscow Mathematical Journal
, 2001
"... We discuss statistical mechanics on nonamenable graphs, and we study the features of the phase transition, which are due to nonamenability. For the Ising model on the usual lattice it is known that uctuations of magnetization are much less likely in the states with nonzero magnetic eld than in th ..."
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Cited by 13 (0 self)
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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, nonamenable 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
 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 ..."
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Cited by 1 (1 self)
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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
"... Abstract. We consider a nearestneighbor four state hardcore (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 ..."
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Abstract. We consider a nearestneighbor four state hardcore (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