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28 March 2024
 
  » arxiv » 1512.3635

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Marginal dimensions of the Potts model with invisible states
M. Krasnytska ; P. Sarkanych ; B. Berche ; Yu. Holovatch ; R. Kenna ;
Date 11 Dec 2015
AbstractWe 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 $r_c = 3.65(5)$; there is a second-order phase transition there when $r<r_c$ and a first-order one at $r>r_c$. We also analyse the region $1 leq q<2$ 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 $r_{c1}$, the order parameters exhibit discontinuities at temperature $ ilde{t}$ below a critical value $t_c$. But, provided $r>r_{c1}$ is small enough, this discontinuity does not appear at the phase transition, which is continuous and takes place at $t_c$. The larger value $r_{c2}$ marks the point at which the phase transition at $t_c$ changes from second to first order. Thus, for $r_{c1}< r < r_{c2}$, the transition at $t_c$ remains second order while the order parameter has a discontinuity at $ ilde{t}$. As $r$ increases further, $ ilde{t}$ increases, bringing the discontinuity closer to $t_c$. Finally, when $r$ exceeds $r_{c2}$ $ ilde{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.
Source arXiv, 1512.3635
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