Séminaire de groupe
|Corner contribution to cluster numbers|
|Institut Wigner (Budapest)|
|lundi 12 mai 2014 , 10h25|
|Salle de séminaire du groupe de Physique Statistique|
For the two-dimensional $Q$-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number $N_\Gamma$ of clusters that intersect a given contour $\Gamma$. To leading order, $N_\Gamma$ is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of $\Gamma$. These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are not found to be consistent with the values obtained by analytic continuation, as conventionally assumed. We mention possible extension of the results for systems with quenched disorder, as well as for three-dimensional problems.