Non-equilibrium phase diagram for a model with coalescence, evaporation and deposition

TL;DR

This paper investigates a lattice model with coalescence, evaporation, and deposition, revealing a phase transition between a growing phase with infinite mass and an exponential phase with finite mass, supported by rigorous bounds and asymptotics.

Contribution

It provides a rigorous analysis of the phase diagram for a coalescence-evaporation-deposition model across all dimensions, including bounds and asymptotic behaviors.

Findings

Identifies a phase transition between growing and exponential phases.

Establishes rigorous bounds on the critical curve.

Derives asymptotic behaviors for large and small deposition rates.

Abstract

We study a d-dimensional lattice model of diffusing coalescing massive particles, with two parameters controlling deposition and evaporation of monomers. The unique stationary distribution for the system exhibits a phase transition in all dimensions d greater or equal to one between a growing phase, in which the expected mass is infinite at each site, and an exponential phase in which the expected mass is finite. We establish rigorous upper and lower bounds on the critical curve describing the phase transition for this system, and some asymptotics for large or small deposition rates.