热力学相变与拓扑相变：Kertész线上的尖点
Thermodynamic versus Topological Phase Transitions: Cusp in the Kertész Line
摘要：
本文研究了在外场$h$存在下，居里-外斯-波茨模型在（逆）温度$β$下的相变.这些过渡的热力学和拓扑方面被认为是。对于第一个方面，我们补充了以前的结果，给出了$β$ -$h$平面中热力学跃迁线的显式方程以及磁化强度的跃变（对于$q \geqslant 3)$）。后一个方面的签名的特点是在这里的一个巨大的组件的Fortuin-Kasteleyn型表示模型的集群中的存在与否。我们给出了（在$β$ -$h$平面内）分离这两种行为的Kertész线方程。因此，我们得到，这条线的展品，只要$q \geqslant 3$，一个非常有趣的尖点，它从热力学过渡线分离。
英文摘要：
We present a study of phase transitions of the Curie--Weiss Potts model at (inverse) temperature $β$, in presence of an external field $h$. Both thermodynamic and topological aspects of these transitions are considered. For the first aspect we complement previous results and give an explicit equation of the thermodynamic transition line in the $β$--$h$ plane as well as the magnitude of the jump of the magnetization (for $q \geqslant 3)$. The signature of the latter aspect is characterized here by the presence or not of a giant component in the clusters of a Fortuin--Kasteleyn type representation of the model. We give the equation of the Kertész line separating (in the $β$--$h$ plane) the two behaviours. As a result, we get that this line exhibits, as soon as $q \geqslant 3$, a very interesting cusp where it separates from the thermodynamic transition line.
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