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

TL;DR

This paper explores the application of conformal field theory, Coulomb gas mappings, and stochastic Loewner evolution to understand critical phenomena in percolation and self-avoiding walks, linking statistical physics with quantum field theories.

Contribution

It introduces recent and older ideas from conformal field theory and related methods to analyze critical states in percolation and self-avoiding walks, connecting them to quantum field theories.

Findings

Insights into conformal invariance in critical models

Connections between statistical physics problems and quantum field theories

Application of stochastic Loewner evolution to these 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.