Tree-hierarchy of DNA and distribution of Holliday junctions
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Biology"
DOI: 10.1007/s00285-017-1136-3
Abstract: We define a DNA as a sequence of $$\pm 1$$±1’s and embed it on a path of Cayley tree. Using group representation of the Cayley tree, we give a hierarchy of a countable set of… read more here.
Keywords: hierarchy dna; set dnas; holliday junctions; tree hierarchy ... See more keywords
Spherical Model on a Cayley Tree: Large Deviations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Statistical Physics"
DOI: 10.1007/s10955-016-1696-4
Abstract: We study the spherical model of a ferromagnet on a Cayley tree and show that in the case of empty boundary conditions a ferromagnetic phase transition takes place at the critical temperature $$T_\mathrm{c} =\frac{6\sqrt{2}}{5}J$$Tc=625J, where… read more here.
Keywords: temperature; cayley; spherical model; frac ... See more keywords
A model with uncountable set of spin values on a Cayley tree: phase transitions
Sign Up to like & getrecommendations! Published in 2017 at "Positivity"
DOI: 10.1007/s11117-016-0445-x
Abstract: In this paper we consider a model with nearest-neighbor interactions and with the set [0,1] of spin values, on a Cayley tree of order two. This model depends on two parameters $$n\in \mathbb N$$n∈N and… read more here.
Keywords: values cayley; model; set spin; spin values ... See more keywords
Explicit construction of the eigenvectors and eigenvalues of the graph Laplacian on the Cayley tree
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DOI: 10.1016/j.laa.2019.10.023
Abstract: Abstract A generalized Fourier analysis on arbitrary graphs calls for a detailed knowledge of the eigenvectors of the graph Laplacian. Using the symmetries of the Cayley tree, we recursively construct the family of eigenvectors with… read more here.
Keywords: construction eigenvectors; graph laplacian; eigenvectors eigenvalues; cayley tree ... See more keywords
On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Statistical Mechanics: Theory and Experiment"
DOI: 10.1088/1742-5468/ab270b
Abstract: The paper concerns the $q$-state Potts model (i.e., with spin values in $\{1,\dots,q\}$) on a Cayley tree $\mathbb{T}^k$ of degree $k\geq 2$ (i.e., with $k+1$ edges emanating from each vertex) in an external (possibly random)… read more here.
Keywords: uniqueness gibbs; field; external field; model ... See more keywords
Phase diagrams of lattice models on Cayley tree and chandelier network: a review
Sign Up to like & getrecommendations! Published in 2022 at "Condensed Matter Physics"
DOI: 10.5488/cmp.25.32501
Abstract: The main purpose of this review paper is to give systematically all the known results on phase diagrams corresponding to lattice models (Ising and Potts) on Cayley tree (or Bethe lattice) and chandelier networks. A… read more here.
Keywords: cayley tree; chandelier network; phase diagrams; lattice models ... See more keywords