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Bethe lattice

Known as: Cayley tree, Lattice 
A Bethe lattice or Cayley tree (a particular kind of Cayley graph), introduced by Hans Bethe in 1935, is an infinite connected cycle-free graph where… 
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Related topics

Related topics

5 relations
Covering spaceFuchsian groupLattice model (physics)Percolation theory

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2013
Highly Cited
2013
Description of the Translation-Invariant Splitting Gibbs Measures for the Potts Model on a Cayley Tree
For the $$q$$q-state Potts model on a Cayley tree of order $$k\ge 2$$k≥2 it is well-known that at sufficiently low temperatures… 
2010
2010
Exact Solution of a Generalized ANNNI Model on a Cayley Tree
We consider the Ising model on a rooted Cayley tree of order two with nearest neighbor interactions and competing next nearest… 
Highly Cited
2007
Highly Cited
2007
On p-adic Gibbs measures of the countable state Potts model on the Cayley tree
In this paper we consider the countable state p-adic Potts model on the Cayley tree. A construction of p-adic Gibbs measures… 
2007
2007
Potts glass on random graphs
We solve the q-state Potts model with anti-ferromagnetic interactions on large random lattices of finite coordination. Due to the… 
1997
1997
Описание периодических крайних гиббсовских мер некоторых решеточных моделей на дереве Кэли@@@Discription of periodic extreme Gibbs measures of some lattice models on the Cayley tree
Highly Cited
1990
Highly Cited
1990
Abelian sandpile model on the bethe lattice
The authors study Bak, Tang and Wiesenfeld's Abelian sandpile model (1987) of self-organised criticality on the Bethe lattice… 
1990
1990
Lyapunov exponents of large, sparse random matrices and the problem of directed polymers with complex random weights
We present results on two different problems: the Lyapunov exponent of large, sparse random matrices and the problem of polymers… 
Highly Cited
1984
Highly Cited
1984
Topological properties of percolation clusters
Percolation properties, including the total cluster mass S, the shell mass B, and the linear geometrical size R, are studied as a… 
Highly Cited
1983
Highly Cited
1983
The localization transition on the Bethe lattice
We present exact results concerning the localization transition on the Bethe lattice. In a certain number of situations, we prove… 
Highly Cited
1981
Highly Cited
1981
Modulated phase of an ising system with competing interactions on a Cayley tree
A system with competing nearest-neighbour and next-nearest-neighbour interactions is considered on a Cayley tree. The phase… 
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