# The finite density scaling laws of condensation phase transition in zero range processes on scale-free networks

## TL;DR

This paper investigates how finite density influences the condensation phase transition in zero-range processes on scale-free networks, providing analytical scaling laws and validating them through simulations.

## Contribution

It introduces analytical scaling laws for finite density effects in zero-range processes on scale-free networks and explores the relaxation dynamics of the phase transition.

## Key findings

- Predicted density scaling laws for steady state occupation numbers.
- Derived a scaling law for relaxation dynamics.
- Validated predictions with Monte Carlo simulations.

## Abstract

The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks. A real space complete condensation phase transition in the stationary state may occur. We have studied the finite density effects of the condensation transition in both the stationary and dynamical zero-range process on scale-free networks. By means of grand canonical ensemble method, we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state. We further explore the relaxation dynamics of the condensation phase transition. By applying the hierarchical evolution and scaling ansatz, a scaling law for the relaxation dynamics is predicted. Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.