## Abstract

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.

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 language | English |
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Article number | 385002 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 46 |

Issue number | 38 |

Early online date | 5 Sep 2013 |

DOIs | |

Publication status | Published - 27 Sep 2013 |

## Keywords

- mathematical physics