Supercluster states and phase transitions in aggregation-fragmentation processes

TL;DR

This paper investigates the formation of supercluster states and phase transitions in aggregation-fragmentation processes, revealing critical exponents and the nature of transitions through theoretical and numerical analysis.

Contribution

It introduces a novel analysis of supercluster states in aggregation-fragmentation models, extending beyond traditional fluctuation tools to determine critical exponents.

Findings

Supercluster states are non-extensive jammed states arising under certain conditions.

The study identifies continuous and discontinuous phase transitions.

Theoretical predictions align well with numerical simulations.

Abstract

We study the evolution of aggregates triggered by collisions with monomers that either lead to the attachment of monomers or the break-up of aggregates into constituting monomers. Depending on parameters quantifying addition and break-up rates, the system falls into a jammed or a steady state. Supercluster states (SCSs) are very peculiar non-extensive jammed states that also arise in some models. Fluctuations underlie the formation of the SCSs. Conventional tools, such as the van Kampen expansion, apply to small fluctuations. We go beyond the van Kampen expansion and determine a set of critical exponents quantifying SCSs. We observe continuous and discontinuous phase transitions between the states. Our theoretical predictions are in good agreement with numerical results.