Conformal Invariance and Percolation

Abstract

These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two disjoint segments of the boundary of a simply connected region; and the mean number of such clusters. No previous familiarity with conformal field theory is assumed, but in the course of the argument many of its important concepts are introduced in as simple a manner as possible. A brief account is also given of some recent alternative approaches to deriving these kinds of result.

Lectures delivered at Chuo University, Tokyo, March 2001; 39 pages; corrected references for Section 7.3 added

Cited by in corpus (26)

• Measurement-driven entanglement transition in hybrid quantum circuits
• Recent advances in percolation theory and its applications
• 2D growth processes: SLE and Loewner chains
• Conformal Field Theories of Stochastic Loewner Evolutions
• From Percolation to Logarithmic Conformal Field Theory
• Euler integrals for commuting SLEs
• Excursion decompositions for $\SLE$ and Watts' crossing formula
• Conformal Random Geometry
• The Full Scaling Limit of Two-Dimensional Critical Percolation
• On the Percolation BCFT and the Crossing Probability of Watts
• Critical percolation in annuli and $SL{E}_6$
• Anchored Critical Percolation Clusters and 2-D Electrostatics
• A formula for crossing probabilities of critical systems inside polygons
• Rectangular amplitudes, conformal blocks, and applications to loop models
• Coset Graphs in Bulk and Boundary Logarithmic Minimal Models
• Proposal for a CFT interpretation of Watts' differential equation for percolation
• SLE(6) and CLE(6) from Critical Percolation
• Potts model on recursive lattices: some new exact results
• W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)
• Duality and Fisher zeros in the 2D Potts model on square lattice
• The high temperature Ising model on the triangular lattice is a critical percolation model
• The expected number of critical percolation clusters intersecting a line segment
• Hopf and Frobenius algebras in conformal field theory
• Bessel process, Schramm-Loewner evolution, and Dyson model
• Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions
• Continuum Percolation on Disoriented Surfaces: the Problem of Permeable Disks on a Klein Bottle