On the Non-equilibrium Phase Transition in Evaporation-Deposition Models

TL;DR

This paper investigates a non-equilibrium phase transition in a system of diffusing-aggregating particles with deposition and evaporation, combining theoretical and numerical methods to understand the transition between growing and non-growing mass phases.

Contribution

It provides rigorous bounds on the transition point and establishes the universality class of the growing phase, along with a scaling theory near the critical point.

Findings

The growing phase has a constant mass flux asymptotically.

Mass distribution and flux decay exponentially below critical deposition rate.

Numerical results support the scaling laws near the critical point.

Abstract

We study a system of diffusing-aggregating particles with deposition and evaporation of monomers. By combining theoretical and numerical methods, we establish a clearer understanding of the non-equilibrium phase transition known to occur in such systems. The transition is between a growing phase in which the total mass increases for all time and a non-growing phase in which the total mass is bounded. In addition to deriving rigorous bounds on the position of the transition point, we show that the growing phase is in the same universality class as diffusion-aggregation models with deposition but no evaporation. In this regime, the flux of mass in mass space becomes asymptotically constant (as a function of mass) at large times. The magnitude of this flux depends on the evaporation rate but the fact that it is asymptotically constant does not. The associated constant flux relation exactly determines the scaling of the two-point mass correlation function with mass in all dimensions while higher-order mass correlation functions exhibit nonlinear multi-scaling in dimension less than 2. If the deposition rate is below some critical value, a different stationary state is reached at large times characterised by a global balance between evaporation and deposition with a scale-by-scale balance between the mass fluxes due to aggregation and evaporation. Both the mass distribution and the flux decay exponentially in this regime. Finally, we develop a scaling theory of the model near the critical point, which yields non-trivial scaling laws for the critical two-point mass correlation function with mass. These results are well supported by numerical measurements.