On the nonequilibrium phase transition in evaporationdeposition models
Preprint, Article
English
OPEN
Connaughton, Colm
;
Rajesh, R.
;
Zaboronski, Oleg V.
(2010)
We study a system of diffusingaggregating particles with deposition and evaporation of monomers. By combining theoretical and numerical methods, we establish a clearer understanding of the nonequilibrium 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 nongrowing 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 diffusionaggregation 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 twopoint mass correlation function with mass in all dimensions while higher order mass correlation functions exhibit nonlinear multiscaling in dimension less than two. If the deposition rate is below some critical value, a different stationary state is reached at large times characterized by a global balance between evaporation and deposition with a scalebyscale 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 nontrivial scaling laws for the critical twopoint mass correlation function with mass. These results are well supported by numerical measurements.

References
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