Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

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Articles dans des revues à comité de lecture

Marginal dimensions of the Potts model with invisible states
M. Krasnytska, P. Sarkanych, B. Berche, Holovatch Yu., R. Kenna
J. Phys. A: Math. Theor. 49 (2016) 255001
DOI : 10.1088/1751-8113/49/25/255001
ArXiv : arxiv:1512.03635 [PDF]

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 Zq-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 rc=3.65(5); there is a second-order phase transition there when rrc. We also analyse the region 1≤q<2 and show that the change from second to first order there is manifest through a new mechanism involving {\emph{two}} marginal values of r. The q=1 limit gives bond percolation and some intermediary values also have known physical realisations. Above the lower value rc1, the order parameters exhibit discontinuities at temperature t~ below a critical value tc. But, provided r>rc1 is small enough, this discontinuity does not appear at the phase transition, which is continuous and takes place at tc. The larger value rc2 marks the point at which the phase transition at tc changes from second to first order. Thus, for rc1

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