Phase Transition in a Conserved-Mass Model of Aggregation and Dissociation

TL;DR

This paper introduces a mass-conserving aggregation-dissociation model exhibiting a phase transition from exponential to power-law mass distributions, analyzed through mean field theory and numerical simulations.

Contribution

It presents a novel model with dissociation dynamics that induces a phase transition in mass distribution, extending understanding of aggregation phenomena.

Findings

Identifies a phase transition between exponential and power-law mass distributions.

Demonstrates coexistence of infinite aggregate with power-law distributed masses.

Provides analytical and numerical evidence of the transition across dimensions.

Abstract

We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a striking behaviour in the steady state. As the parameters are varied, the system undergoes a dynamical phase transition in all dimensions. In one phase the mass distribution decays exponentially for large mass whereas in the other phase there is a power law distribution of masses which coexists with an infinite mass aggregate. The model is investigated analytically within mean field theory, and numerically in one dimension.