Many universality classes in an interface model restricted to non-negative heights

TL;DR

This paper introduces a one-dimensional stochastic interface model with multiple control parameters, revealing a rich variety of phase transitions and universality classes, including Edwards-Wilkinson, KPZ, directed percolation, and novel behaviors.

Contribution

It presents a new simple model that exhibits a wide range of phase transitions and universality classes, including novel types not previously observed.

Findings

Identification of multiple universality classes including EW, KPZ, and DP.

Discovery of novel behaviors in pushed fronts and interface detachment transitions.

Mapping of the model to avalanche propagation in a directed Oslo rice pile.

Abstract

We present a simple one dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site $x$ and time $t$, an integer $n(x,t)$ satisfies a linear interface equation with added random noise. Depending on the control parameters, this noise may or may not satisfy the detailed balance condition, so that the growing interfaces are in the Edwards-Wilkinson (EW) or in the Kardar-Parisi-Zhang (KPZ) universality class. In addition, there is also a constraint $n(x,t) \geq 0$. Points $x$ where $n>0$ on one side and $n=0$ on the other are called ``fronts". These fronts can be ``pushed" or ``pulled", depending on the control parameters. For pulled fronts, the lateral spreading is in the directed percolation (DP) universality class, while it is of a novel type for pushed fronts, with yet another novel behavior in between. In the DP case, the activity at each active site can in general be arbitrarily large, in contrast to previous realizations of DP. Finally, we find two different types of transitions when the interface detaches from the line $n=0$ (with $\langle n(x,t)\rangle \to$ const on one side, and $\to \infty$ on the other), again with new universality classes. We also discuss a mapping of this model to the avalanche propagation in a directed Oslo rice pile model in specially prepared backgrounds.