6533b82cfe1ef96bd128f679

RESEARCH PRODUCT

Corner contribution to cluster numbers in the Potts model

Martin WeigelMartin WeigelEren Metin ElçiEren Metin ElçiIstván KovácsFerenc Iglói

subject

PhysicsPhase transitionLogarithmStatistical Mechanics (cond-mat.stat-mech)Conformal field theoryAnalytic continuationOrder (ring theory)FOS: Physical sciencesCondensed Matter PhysicsElectronic Optical and Magnetic MaterialsCluster (physics)Condensed Matter::Statistical MechanicsCondensed Matter - Statistical MechanicsMathematical physicsSpin-½Potts model

description

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.

yearjournalcountryeditionlanguage
2013-11-17
https://dx.doi.org/10.48550/arxiv.1311.4186