### Abstract

We present the exact solution of the 1D classical short-range Potts model with invisible states. Besides the q states of the ordinary Potts model, this possesses r additional states which contribute to the entropy, but not to the interaction energy. We determine the partition function, using the transfer-matrix method, in the general case of two ordering fields: h_{1} acting on a visible state and h_{2} on an invisible state. We analyse its zeros in the complex-temperature plane in the case that h_{1}=0. When Imh_{2}=0 and r≥0, these zeros accumulate along a line that intersects the real temperature axis at the origin. This corresponds to the usual “phase transition” in a 1D system. However, for Imh_{2}≠0 or r<0, the line of zeros intersects the positive part of the real temperature axis, which signals the existence of a phase transition at non-zero temperature.

Original language | English |
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Pages (from-to) | 3589-3593 |

Number of pages | 5 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 381 |

Issue number | 41 |

Early online date | 1 Sep 2017 |

DOIs | |

Publication status | Published - 5 Nov 2017 |

### Keywords

- Invisible states
- Partition function zeros
- Phase transitions
- Potts model

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*381*(41), 3589-3593. https://doi.org/10.1016/j.physleta.2017.08.063