Nonlocal growth processes and conformal invariance

TL;DR

This paper introduces a new nonlocal growth process model exhibiting conformal invariance, expanding the class of stochastic models with this property and analyzing their phase diagrams and critical exponents.

Contribution

It presents the raise and strip model with nonlocal desorption, showing it shares the phase diagram with the raise and peel model but has different critical exponents.

Findings

The model exhibits a phase diagram with gapped, critical, and gapless phases.

Critical exponents differ from the raise and peel model.

Suggests a broader class of conformally invariant stochastic models.

Abstract

Up to now the raise and peel model was the single known example of a one-dimensional stochastic process where one can observe conformal invariance. The model has one-parameter. Depending on its value one has a gapped phase, a critical point where one has conformal invariance and a gapless phase with changing values of the dynamical critical exponent $z$. In this model, adsorption is local but desorption is not. The raise and strip model presented here in which desorption is also nonlocal, has the same phase diagram. The critical exponents are different as are some physical properties of the model. Our study suggest the possible existence of a whole class of stochastic models in which one can observe conformal invariance.