Uniqueness of the Gibbs Measure for the Anti-ferromagnetic Potts Model on the Infinite Δ-Regular Tree for Large Δ

Uniqueness of the Gibbs Measure for the Anti-ferromagnetic Potts Model on the Infinite Δ-Regular Tree for Large Δ

In this paper we prove that for any integer q ≥ 5 , the anti-ferromagnetic q -state Potts model on the infinite Δ -regular tree has a unique Gibbs measure for all edge interaction parameters w ∈ [ 1 - q / Δ , 1 ) , provided Δ is large enough. This confirms a longstanding folklore conjecture.

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Veröffentlicht in:Journal of statistical physics 2023-08, Vol.190 (8), Article 140
Hauptverfasser: Bencs, Ferenc, Boer, David de, Buys, Pjotr, Regts, Guus
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Zusammenfassung:In this paper we prove that for any integer q ≥ 5 , the anti-ferromagnetic q -state Potts model on the infinite Δ -regular tree has a unique Gibbs measure for all edge interaction parameters w ∈ [ 1 - q / Δ , 1 ) , provided Δ is large enough. This confirms a longstanding folklore conjecture.
ISSN:1572-9613
1572-9613
DOI:10.1007/s10955-023-03145-z