Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation and Fragmentation

TL;DR

This paper investigates a nonequilibrium phase transition in a model combining diffusion, aggregation, and fragmentation, revealing distinct phases with exponential or power-law mass distributions and identifying new fixed points in interface fluctuation behavior.

Contribution

The study provides an exact solution within mean field approximation, exact steady states in 1D limits, and numerical analysis of critical exponents and phase diagrams, including generalizations with arbitrary fragmentation kernels.

Findings

Distinct phases with exponential and power-law mass distributions

Exact solutions and phase diagrams in various dimensions

Identification of two new fixed points in interface fluctuation dynamics

Abstract

We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass distribution decays exponentially for large mass in one phase. On the contrary, in the other phase it has a power law tail and in addition an infinite aggregate. The model is solved exactly within a mean field approximation which keeps track of the distribution of masses. In one dimension, by mapping to an equivalent lattice gas model, exact steady states are obtained in two extreme limits of the parameter space. Critical exponents and the phase diagram are obtained numerically in one dimension. We also study the time dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exponent $\chi$ and the dynamical exponent z analytically in some limits and numerically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statistical mechanics.