Potts models with invisible states on general Bethe lattices

N. Ananikian, N. Izmailyan, D.A. Johnston, Ralph Kenna, R.P.K.C.M. Ranasinghe

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    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, [equation - see note] invisible states are required to manifest the equivalent Blume–Emery–Griffiths tricriticality. When z = 3, the 3-regular random graph result is recovered, while z → ∞ delivers the Bragg–Williams (mean-field) result. The equation in this abstract does not display correctly on this platform, please see http://dx.doi.org/10.1088/1751-8113/46/38/385002 for the full abstract.
    Original languageEnglish
    Article number385002
    JournalJournal of Physics A: Mathematical and Theoretical
    Issue number38
    Publication statusPublished - 2013

    Bibliographical note

    The full text is available free from the link given. The published version can be found at http://dx.doi.org/10.1088/1751-8113/46/38/385002.


    • lattice systems
    • Potts
    • Bethe lattices


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