Thermodynamic versus Topological Phase Transitions: Cusp in the Kertész Line

Philippe Blanchard (1) , Daniel Gandolfo (2, 3) , Jean Ruiz (2, 3) , Marc Wouts (4, 5)

1 BIBOS - Theoretische Physik und BiBoS [Bielefeld]
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332
4 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
5 MODAL'X - Modélisation aléatoire de Paris X

We present a study of phase transitions of the Curie--Weiss Potts model at (inverse) temperature $\beta$, 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 $\beta$--$h$ 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 $\beta$--$h$ 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.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Philippe Blanchard, Daniel Gandolfo, Jean Ruiz, Marc Wouts. Thermodynamic versus Topological Phase Transitions: Cusp in the Kertész Line. EPL - Europhysics Letters, 2008, 82, pp.50003. ⟨10.1209/0295-5075/82/50003⟩. ⟨hal-00263693v2⟩