The scaling limit of two cluster boundaries in critical lattice models
Adam Gamsa, John Cardy
Abstract
The probability that a point is to one side of a curve in Schramm-Loewner evolution (SLE) can be obtained alternatively using boundary conformal field theory (BCFT). We extend the BCFT approach to treat two curves, forming, for example, the left and right boundaries of a cluster. This proves to correspond to a generalisation to SLE(kappa,rho), with rho=2. We derive the probabilities that a given point lies between two curves or to one side of both. We find analytic solutions for the cases kappa=0,2,4,8/3,8. The result for kappa=6 leads to predictions for the current distribution at the plateau transition in the semiclassical approximation to the quantum Hall effect.
Create a lesson
Related papers
2-Morita Theory of E2-Algebras and Module Categories
Rongge Xu, Holiverse Yang
Multiscale Loop Vertex Expansion for Cumulants, the ϕ42 Model
Vincent Rivasseau
Quasi-polynomiality and N-point functions of single connected leaky completed Hurwitz numbers
Chongyu Wang, Chenglang Yang
Coupled stochastic variational principles for multiscale surface gravity waves -- Part I: theoretical framework
Etienne Mémin, Arnaud Debussche
The Sharp Spectral Transition for Almost Mathieu Operators via Alternating Resonances
Jiawei He, Xueyin Wang
Dynamical classical-field limit of Bosonic Gibbs states: Renormalized Hartree NLS correlations in 2D and 3D
Phan Thành Nam, Rongchan Zhu, Xiangchan Zhu