Interfaces in critical Z(N) spin models: suitable candidates for SLE curves in non-minimal conformal field theories.
Lundi 22/10/2007, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
The Schramm-Loewner evolution (SLE) is a powerful tool to describe
fractal interfaces in 2D critical statistical systems. Yet the application
of SLE is well established for statistical systems described by quantum
field theories satisfying only conformal invariance, the so called minimal
conformal field theories (CFTs). In this talk I will consider some
interface which can be defined in N-states spin models with cyclic $Z_N$
symmetry. The phase diagram of these lattice models presents self-dual
critical points described by non-minimal CFTs where the role of the $Z_N$
symmetry beside the conformal one should be taken into account. Using CFT
predictions, we show that these interfaces are suitable candidates for SLE
curves in non-minimal CFTs.