Conformal invariant growth models
by Francisco C. Alcaraz
Abstract: Most of the critical interacting systems, at equilibrium, besides scale invariant are also conformal invariant. This symmetry gives, in the two dimensional case, a huge amount of information concerning the long-distance physics of these systems. On the other hand, most of the non equilibrium stochastic systems, at criticality, although scale invariant, do not show the space-time conformal symmetry. A known exception is the Raise and Peel model (RPM), that describes the fluctuations of the interface of a growth model in one dimension with local adsorption and non-local desorption. After a short presentation of the RPM model we are going to present a generalization of the model containing an additional parameter \(p\). The RPM model is recovered at \(p = 1\). We show that the model is conformal invariant in the whole region \(0 < p \leq 2\). At the special point \(p = 2\), the model has an adsorbing state. At this point an interesting phenomena happens. We are going to show that although the absorbing state is present, the system prefers to be in a quasi-stationary state with fluctuations ruled by an underlying conformal invariant model.