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

TL;DR

This paper investigates a solvable asymmetric avalanche model, revealing a transition from KPZ to tilted interface critical behavior, and provides exact expressions for avalanche sizes and critical exponents.

Contribution

It introduces a discrete-time formulation of the model and maps different avalanche regimes onto driven interface problems, identifying a novel transition in critical behavior.

Findings

Exact expression for average avalanche size as a function of parameters

Identification of a transition from KPZ to tilted interface behavior

Critical exponents that violate known scaling relations when  2

Abstract

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 $\alpha \ne 2$.