Conformal invariance and its breaking in a stochastic model of a fluctuating interface

Using Monte-Carlo simulations on large lattices, we study the effects of changing the parameter u (the ratio of the adsorption and desorption rates) of the raise and peel model. This is a nonlocal stochastic model of a fluctuating interface. We show that for 0 < u < 1 the system is massive, for u = 1 it is massless and conformal invariant. For u > 1 the conformal invariance is broken. The system is in a scale invariant phase with the dynamical critical exponent z and other critical exponents varying continuously with u. As far as we know it is the first example of a system which shows such a behavior. Moreover in the broken phase, the critical exponents vary continuously with the parameter u. This stays true also for the critical exponent τ which characterizes the probability distribution function of avalanches (the critical exponent D staying unchanged).