Critical behaviour in a non-local interface model

The Raise and Peel model is a recently proposed one-dimensional statistical model describing a fluctuating interface. The evolution of the model follows from the competition between adsorption and desorption processes. The model is non-local due to the possible occurrence of avalanches. At a special ratio of the adsorption-desorption rates, the model is integrable and many rigorous results are known. Off the critical point, the phase diagram and scaling properties are not known. In this paper, we search for indications of phase transition studying the gap in the spectrum of the non-Henrmitian generator of the stochastic interface evolution. We present results for the gap obtained from exact diagonalization and from Monte Carlo estimates derived from temporal correlations of various observables.