Uniqueness of the Gibbs measure for the $4$-state anti-ferromagnetic Potts model on the regular tree
| Autor: | David de Boer, Pjotr Buys, Guus Regts |
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| Přispěvatelé: | Analysis (KDV, FNWI), KdV Other Research (FNWI), Algebra, Geometry & Mathematical Physics (KDV, FNWI) |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences Discrete Mathematics (cs.DM) Applied Mathematics Probability (math.PR) FOS: Physical sciences 82B20 (Primary) 60K35 05C99 (Secondary) Mathematical Physics (math-ph) Theoretical Computer Science Computational Theory and Mathematics FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Mathematics - Probability Mathematical Physics Computer Science - Discrete Mathematics |
| Zdroj: | Combinatorics Probability and Computing, 32(1), 158-182. Cambridge University Press |
| ISSN: | 0963-5483 |
| DOI: | 10.48550/arxiv.2011.05638 |
| Popis: | We show that the $4$-state anti-ferromagnetic Potts model with interaction parameter $w\in(0,1)$ on the infinite $(d+1)$-regular tree has a unique Gibbs measure if $w\geq 1-\frac{4}{d+1}$ for all $d\geq 4$. This is tight since it is known that there are multiple Gibbs measures when $0\leq w Subsection 1.2 and Section have been merged and slightly rewritten. Proof of Lemma 1.3 has been moved to an appendix, fixed a small mistake in the proof of this lemma. Some small other changes have been made. No significant changes. Accepted in CPC |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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