Off-critical parafermions and the winding angle distribution of the O(n) model
Andrew Elvey Price, Jan de Gier, Anthony J Guttmann, Alexander Lee
Journal of Physics A - Mathematical and General | IOP PUBLISHING LTD | Published : 2012
Using an off-critical deformation of the identity of Duminil-Copin and Smirnov, we prove a relationship between half-plane surface critical exponents γ and γ as well as wedge critical exponents γ (α) and γ (α) and the exponent characterizing the winding angle distribution of the O(n) model in the half-plane, or more generally in a wedge of wedge-angle α. We assume only the existence of these exponents and, for some values of n, the conjectured value of the critical point. If we assume their values as predicted by conformal field theory, one gets complete agreement with the conjectured winding angle distribution, as obtained by CFT and Coulomb gas arguments. We also prove the exponent i..View full abstract
Awarded by NSF
We are grateful for financial support from the Australian Research Council (ARC). This work was carried out during the visit of three of the authors to the US Mathematical Sciences Research Institute (MSRI, USA), during the Spring 2012 Random Spatial Processes Program. The authors thank the institute for its hospitality and the NSF (grant DMS-0932078) for its financial support. AJG wishes to thank Neal Madras and Mireille Bousquet-Melou for helpful discussions.