78 citations
17 papers
Phase transition and Gibbs Measures of Vannimenus model on semi-infinite Cayley tree of order three
Hasan Akin
Ising model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree has long been studied but there are still many problems untouched. T…
Using New Approaches to obtain Gibbs Measures of Vannimenus model on a Cayley tree
Hasan Akin
In this paper, we consider Vannimenus model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree. For this model we define Markov ran…
Decompositions of Cellular Binomial Ideals
Zekiye Sahin Eser, Laura Felicia Matusevich
Without any restrictions on the base field, we compute the hull and prove a conjecture of Eisenbud and Sturmfels giving an unmixed decomposition of a cellular binomial ideal. Over…
On non-Archimedean recurrence equations and their applications
Farrukh Mukhamedov, Hasan Akin
In the present paper we study stability of recurrence equations (which in particular case contain a dynamics of rational functions) generated by contractive functions defined on an…
Contraction Formulas For Kirchhoff And Wiener Indices
Zubeyir Cinkir
We establish several contraction formulas for Kirchhoff index. We relate Kirchhoff index with some other metrized graph invariants. By applying our contraction formulas successivel…
Phase transitions for -adic Potts model on the Cayley tree of order three
Farrukh Mukhamedov, Hasan Akin
In the present paper, we study a phase transition problem for the -state -adic Potts model over the Cayley tree of order three. We consider a more general notion of -adic…