Towards conformal invariance of 2D lattice models

Abstract

Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and dimensions. We will discuss how to prove the conformal invariance conjectures, especially in relation to Schramm-Loewner Evolution.

ICM 2006 paper with a few typos corrected

References in corpus (6)

• The Random-Cluster Model
• The dimension of the SLE curves
• 2D growth processes: SLE and Loewner chains
• Scaling Limits for Minimal and Random Spanning Trees in Two Dimensions
• The Full Scaling Limit of Two-Dimensional Critical Percolation
• Some recent aspects of random conformally invariant systems

Cited by in corpus (8)

• Recent advances in percolation theory and its applications
• Conformal Invariance in the Long-Range Ising Model
• Holomorphic Parafermions in the Potts model and SLE
• Multiple SLE type scaling limits: from local to global
• Strong path convergence from Loewner driving function convergence
• Schramm--Loewner-evolution-type growth processes corresponding to Wess--Zumino--Witten theories
• Hypotrochoids in conformal restriction systems and Virasoro descendants
• Exact critical-temperature bounds for two-dimensional Ising models