A conformal invariant growth model

TL;DR

This paper introduces a one-parameter extension of the raise and peel growth model, exhibiting conformal invariance in the finite-size scaling limit and enabling the study of nonlocal observable universality.

Contribution

It presents a novel one-parameter conformal invariant growth model with nonlocal desorption rates, expanding understanding of universality in such systems.

Findings

Model is conformal invariant in the finite-size scaling limit.

The parameter affects the sound velocity but not the conformal invariance.

At the boundary, the stationary state becomes absorbing and conformal invariance is lost.

Abstract

We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interface and change its shape. The adsorption rates are local but the desorption rates are non-local, they depend not only on the cluster hit by the tile but also on the total number of peaks (local maxima) belonging to all the clusters of the configuration. The domain of the parameter is determined by the condition that the rates are non-negative. In the finite-size scaling limit, the model is conformal invariant in the whole open domain. The parameter appears in the sound velocity only. At the boundary of the domain, the stationary state is an adsorbing state and conformal invariance is lost. The model allows to check the universality of nonlocal observables in the raise and peel model. An example is given.