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arXiv · 0803.1921

Thermodynamic versus Topological Phase Transitions: Cusp in the Kertész Line

Philippe Blanchard·Daniel Gandolfo·Jean Ruiz·Marc Wouts
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Abstract

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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Philippe Blanchard, Daniel Gandolfo, Jean Ruiz, Marc Wouts. 2008-09-02. Thermodynamic versus Topological Phase Transitions: Cusp in the Kertész Line. https://doi.org/10.1209/0295-5075/82/50003

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