Potts models with invisible states on general Bethe lattices

Nerses Ananikian, Nikolay Izmailyan, Desmond Alexander Johnston, Ralph Kenna, R Ranasinghe

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The number of so-called invisible states which need to be added to the
q-state Potts model to transmute its phase transition from continuous to first
order has attracted recent attention. In the q = 2 case, a Bragg–Williams
(mean-field) approach necessitates four such invisible states while a 3-regular
random graph formalism requires seventeen. In both of these cases, the
changeover from second- to first-order behaviour induced by the invisible
states is identified through the tricritical point of an equivalent Blume–Emery–
Griffiths model. Here we investigate the generalized Potts model on a Bethe
lattice with z neighbours. We show that, in the q = 2 case, rc (z)
invisible states are required to manifest the equivalent Blume–Emery–Griffiths
tricriticality. When z = 3, the 3-regular random graph result is recovered, while
infinite z delivers the Bragg–Williams (mean-field) result.
Original languageEnglish
Article number385002
Number of pages10
JournalJournal of Physics A: Mathematical and Theoretical
Issue number38
Early online date5 Sept 2013
Publication statusPublished - 27 Sept 2013


  • mathematical physics


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