Conformal Invariance in Percolation, Self-Avoiding Walks and Related Problems

Abstract

Over the years, problems like percolation and self-avoiding walks have provided important testing grounds for our understanding of the nature of the critical state. I describe some very recent ideas, as well as some older ones, which cast light both on these problems themselves and on the quantum field theories to which they correspond. These ideas come from conformal field theory, Coulomb gas mappings, and stochastic Loewner evolution.

Plenary talk given at TH-2002, Paris. 21 pages, 9 figures

References in corpus (1)

• SLE_k growth processes and conformal field theories

Cited by in corpus (9)

• Unparticle Physics
• The Loewner equation: maps and shapes
• SLE martingales and the Virasoro algebra
• Percolation in self-similar networks
• Domain walls and Schramm-Loewner evolution in the random-field Ising model
• Duality between equilibrium and growing networks
• Fractal Structure of Equipotential Curves on a Continuum Percolation Model
• Critical and multicritical Lee-Yang fixed points in the local potential approximation
• Stochastic Loewner Evolution