### Abstract

Original language | English |
---|---|

Article number | 255001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 25 |

DOIs | |

Publication status | Published - 12 May 2016 |

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### Bibliographical note

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.This document is the author’s post-print version, incorporating any revisions agreed during the peer-review process. Some differences between the published version and this version may remain and you are advised to consult the published version if you wish to cite from it.

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*49*(25), [255001]. https://doi.org/10.1088/1751-8113/49/25/255001

**Marginal dimensions of the Potts model with invisible states.** / Krasnytska, M.; Sarkanych, Petro; Berche, B.; Holovatch, Y.; Kenna, Ralph.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 49, no. 25, 255001. https://doi.org/10.1088/1751-8113/49/25/255001

}

TY - JOUR

T1 - Marginal dimensions of the Potts model with invisible states

AU - Krasnytska, M.

AU - Sarkanych, Petro

AU - Berche, B.

AU - Holovatch, Y.

AU - Kenna, Ralph

N1 - Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders. This document is the author’s post-print version, incorporating any revisions agreed during the peer-review process. Some differences between the published version and this version may remain and you are advised to consult the published version if you wish to cite from it.

PY - 2016/5/12

Y1 - 2016/5/12

N2 - We reconsider the mean-field Potts model with q interacting and r non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the Z q -symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of r at which the order of the phase transition changes. In the q = 2 case, we determine that value to be ${r}_{{\rm{c}}}=3.65(5);$ there is a second-order phase transition there when $r\lt {r}_{{\rm{c}}}$ and a first-order one at $r\gt {r}_{{\rm{c}}}$. We also analyse the region $1\leqslant q\lt 2$ and show that the change from second to first order there is manifest through a new mechanism involving two marginal values of r. The q = 1 limit gives bond percolation. Above the lower value r c1, the order parameters exhibit discontinuities at temperature $\tilde{t}$ below a critical value t c. The larger value r c2 marks the point at which the phase transition at t c changes from second to first order. Thus, for ${r}_{{\rm{c}}1}\lt r\lt {r}_{{\rm{c}}2}$, the transition at t c remains second order while at $\tilde{t}$ the system undergoes a first order phase transition. As r increases further, $\tilde{t}$ increases, bringing the discontinuity closer to t c. Finally, when r exceeds r c2 $\tilde{t}$ coincides with t c and the phase transition becomes first order. This new mechanism indicates how the discontinuity characteristic of first order phase transitions emerges.

AB - We reconsider the mean-field Potts model with q interacting and r non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the Z q -symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of r at which the order of the phase transition changes. In the q = 2 case, we determine that value to be ${r}_{{\rm{c}}}=3.65(5);$ there is a second-order phase transition there when $r\lt {r}_{{\rm{c}}}$ and a first-order one at $r\gt {r}_{{\rm{c}}}$. We also analyse the region $1\leqslant q\lt 2$ and show that the change from second to first order there is manifest through a new mechanism involving two marginal values of r. The q = 1 limit gives bond percolation. Above the lower value r c1, the order parameters exhibit discontinuities at temperature $\tilde{t}$ below a critical value t c. The larger value r c2 marks the point at which the phase transition at t c changes from second to first order. Thus, for ${r}_{{\rm{c}}1}\lt r\lt {r}_{{\rm{c}}2}$, the transition at t c remains second order while at $\tilde{t}$ the system undergoes a first order phase transition. As r increases further, $\tilde{t}$ increases, bringing the discontinuity closer to t c. Finally, when r exceeds r c2 $\tilde{t}$ coincides with t c and the phase transition becomes first order. This new mechanism indicates how the discontinuity characteristic of first order phase transitions emerges.

U2 - 10.1088/1751-8113/49/25/255001

DO - 10.1088/1751-8113/49/25/255001

M3 - Article

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 25

M1 - 255001

ER -