q-state modified Potts model on a Cayley tree and its phase transition in antiferromagnetic region

Hasan Akın

Chaos, Solitons & Fractals, 2025, vol. 199, issue P2

Abstract: We introduce a modified version of the Potts model, characterized by a new Hamiltonian that assigns energy +J when two nearest neighboring spins are identical, and −J when interacting spins differ. This research initializes the q-state modified Potts model on a semi-infinite Cayley tree of order k, utilizing a newly proposed Hamiltonian that promotes dissimilar neighboring spins. This modification, which diverges from the traditional Potts model, addresses the influence of competing interactions pertinent to the antiferromagnetic phase transition regime. Using the cavity method, we construct limiting Gibbs measures by analyzing the associated recurrence equations. The existence of translation-invariant solutions to these relations are further explored using Preston’s approach. Our results demonstrate the existence of phase transitions exclusively in the antiferromagnetic region. Furthermore, through a stability analysis of the dynamical system, we uncover both chaotic and periodic behaviors, highlighting the rich complexity induced by the interplay of non-trivial interactions and the non-amenable geometry of the Cayley tree.

Keywords: Modified Potts model; Gibbs measure; Phase transition; Lyapunov exponent (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925007593
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007593

DOI: 10.1016/j.chaos.2025.116746

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().