Directed Ising type dynamic preroughening transition in one dimensional interfaces

TL;DR

This paper models a directed Ising type phase transition in one-dimensional interfaces, revealing a preroughening transition with initial condition-dependent critical behavior and three distinct steady states.

Contribution

It demonstrates a new realization of DI type transitions in interface relaxation, highlighting the role of initial conditions in critical dynamics.

Findings

Identification of three steady states: rough, flat, and disordered flat.

Observation of a preroughening transition between flat and disordered flat phases.

Critical behavior depends on initial correlations, affecting exponents.

Abstract

We present a realization of directed Ising (DI) type dynamic absorbing state phase transitions in the context of one-dimensional interfaces, such as the relaxation of a step on a vicinal surface. Under the restriction that particle deposition and evaporation can only take place near existing kinks, the interface relaxes into one of three steady states: rough, perfectly ordered flat (OF) without kinks, or disordered flat (DOF) with randomly placed kinks but in perfect up-down alternating order. A DI type dynamic preroughening transition takes place between the OF and DOF phases. At this critical point the asymptotic time evolution is controlled not only by the DI exponents but also by the initial condition. Information about the correlations in the initial state persists and changes the critical exponents.