Searcharxiv⌕ Search

arXiv subjects

Chin Hee Pah

Publications and source records attributed to Chin Hee Pah.

5 recordsLinked to original sources
arXiv2019

On Ground States and Phase Transition for $λ$-Model with the Competing Potts Interactions on Cayley Trees

In this paper, we consider the $λ$-model with nearest neighbor interactions and with competing Potts interactions on the Cayley tree of order-two. We notice that if $λ$-function is taken as a Potts interaction function, then this model contains as a particular case of Potts model with competing interactions on Cayley tree. In this paper, we first describe all ground states of the model. We point out that the Potts model with considered interactions was investigated only numerically, without rigorous (mathematical) proofs. One of the main points of this paper is to propose a measure-theoretical approach for the considered model in more general setting. Furthermore, we find certain conditions for the existence of Gibbs measures corresponding to the model, which allowed to establish the existence of the phase transition.

math-ph↗
arXiv2016

On Ground States and Phase Transitions of $λ$-Model on the Cayley Tree

In the paper, we consider the $λ$-model with spin values $\{1, 2, 3\}$ on the Cayley tree of order two. We first describe ground states of the model. Moreover, we also proved the existence of translation-invariant Gibb measures for the $λ$-model which yield the existence of the phase transition. Lastly, we established the exitance of 2-periodic Gibbs measures for the model.

math-ph↗
arXiv2010

Single Polygon Counting for $m$ Fixed Nodes in Cayley Tree: Two Extremal Cases

We denote a polygon as a connected component in Cayley tree of order 2 containing certain number of fix vertices. We found an exact formula for a polygon counting problem for two cases, in which, for the first case the polygon contain a full connected component of a Cayley tree and for the second case the polygon contain two fixed vertices. From these formulas, which is in the form of finite linear combination of Catalan numbers, one can find the asymptotic estimation for a counting problem.

math.NT↗
arXiv2008

Phase diagram of the three states Potts model with next nearest neighbor interactions on the Bethe lattice

We have found an exact phase diagram of the Potts model with next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the Lifshitz point i.e. $p=1/3$. We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by 2-periodic points of an one dimensional dynamical system lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.

cond-mat.stat-mech↗