2D LATTICE MODELS AND CONFORMAL INVARIANCE

We will give an expository talk comparing two approaches to 2D lattice models of critical phenomena. Developed over two decades ago, Conformal Field Theory led to spectacular predictions for 2D lattice models. While the algebraic framework of CFT is rather solid, rigorous arguments relating it to lattice models were lacking. More recently, a geometric approach involving random SLE curves was proposed by Oded Schramm, and developed by him, Greg Lawler, Wendelin Werner, Steffen Rohde and others. Not only this approach is completely rigorous, it also constructs new objects of physical interest and gives results inaccessible by CFT means.