### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### 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

**Exact solution of a classical short-range spin model with a phase transition in one dimension : The Potts model with invisible states.** / Sarkanych, Petro; Holovatch, Yurij; Kenna, Ralph.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 381, no. 41, pp. 3589-3593. https://doi.org/10.1016/j.physleta.2017.08.063

}

TY - JOUR

T1 - Exact solution of a classical short-range spin model with a phase transition in one dimension

T2 - The Potts model with invisible states

AU - Sarkanych, Petro

AU - Holovatch, Yurij

AU - Kenna, Ralph

PY - 2017/11/5

Y1 - 2017/11/5

N2 - 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: h1 acting on a visible state and h2 on an invisible state. We analyse its zeros in the complex-temperature plane in the case that h1=0. When Imh2=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 Imh2≠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.

AB - 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: h1 acting on a visible state and h2 on an invisible state. We analyse its zeros in the complex-temperature plane in the case that h1=0. When Imh2=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 Imh2≠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.

KW - Invisible states

KW - Partition function zeros

KW - Phase transitions

KW - Potts model

UR - http://www.scopus.com/inward/record.url?scp=85028988102&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2017.08.063

DO - 10.1016/j.physleta.2017.08.063

M3 - Article

VL - 381

SP - 3589

EP - 3593

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

IS - 41

ER -