Abstract: 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: e.g., the critical
percolation cluster a.s. has dimension 91/48 or the number of
self-avoiding length N walks on the hexagonal lattice is
≈ (2+√2)
N/2N(11/32).
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.
