Nonlocal growth processes and conformal invariance
  Up to now the raise and peel model was the single known example of a one-dimensional stochastic process where one can observe conformal invariance. The model has one-parameter.   Depending on its value one has a gapped phase, a critical point where one has conformal invariance and a gapless phase with changing values of the dynamical critical exponent $z$. In this model, adsorption is local but desorption is not. The raise and strip model presented here in which desorption is also nonlocal, has the same phase diagram. The critical exponents are different as are some physical properties of the model. Our study suggest the possible existence of a whole class of stochastic models in which one can observe conformal invariance. 
Francisco C. Alcaraz and Vladimir Rittenberg
cond-mat.stat-mech hep-lat