Gibbs measure for the HC-Blume-Capel model in the case of a "wand" type graph on a Cayley tree
Year: 2026
Type: preprint
Abstract: In this paper, we investigate translation-invariant splitting Gibbs measures (TISGMs) for the HC-Blume-Capel model on a "wand" graph embedded in the Cayley tree of arbitrary order $k \geq 2$. It is known that there is the exact critical value $θ_{cr}$ such that for $θ\geq θ_{cr}$, there exists a unique TISGM, whereas for $θ< θ_{cr}$, precisely three TISGMs exist in the case of a "wand" graph for the given model. In the present paper, we completely solve the (non-)extremality problem for one of these measures for any order $k$ of Cayley tree
Source: arXiv (Cornell University)
Institution: Namangan State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7147745293