Transition from KPZ to Tilted Interface Critical Behavior in a Solvable Asymmetric Avalanche Model

We use a discrete-time formulation to study the asymmetric avalanche process [Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact expression for the average avalanche size of particles as a function of toppling probabilities depending on parameters $\mu$ and $\alpha$. By mapping the model below and above the critical line onto driven interface problems, we show how different regimes of avalanches may lead to different types of critical interface behavior characterized by either annealed or quenched disorders and obtain exactly the related critical exponents which violate a well-known scaling relation when $\alpha \ne 2$.