Gibbs measure for the HC-Blume-Capel model in the case of a "wand" type graph on a Cayley tree
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911555743907840 |
|---|---|
| author | Khatamov, Nosirjon M. Kodirova, Malika A. |
| author_facet | Khatamov, Nosirjon M. Kodirova, Malika A. |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28830 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gibbs measure for the HC-Blume-Capel model in the case of a "wand" type graph on a Cayley tree Khatamov, Nosirjon M. Kodirova, Malika A. Mathematical Physics Probability 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 |
| title | Gibbs measure for the HC-Blume-Capel model in the case of a "wand" type graph on a Cayley tree |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2603.28830 |