Avalanches in the Raise and Peel model in the presence of a wall

TL;DR

This paper studies avalanches in the raise and peel model with a wall, revealing new universality classes and exponents through finite-size scaling, exact diagonalization, and Monte Carlo simulations.

Contribution

It introduces the effect of a wall on avalanche distributions in the raise and peel model, discovering new exponents and conjecturing probability distributions.

Findings

Universality holds for odd number of tiles removed with and without a wall.

A new exponent appears in the presence of a wall for even avalanches.

Conjectured probability distributions are supported by numerical simulations.

Abstract

We investigate a non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For specific values of adsorption ($u_a$) and desorption($u_d$) rates the model shows interesting features. At $u_a = u_d$, the model is described by a conformal field theory (with conformal charge $c=0$) and its stationary probability canbe mapped to the ground state of the XXZ quantum chain. Moreover, for $u_a \geq u_d$, the model shows a phase in which the the avalanche distribution is scale invariant. In this work we study the surface dynamics by looking at avalanche distributions using Finite-size Scaling formalism and explore the effect of adding a wall to the model. The model shows the same universality for the cases with and without a wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations.