Monte Carlo Renormalization Group for Entanglement Percolation

TL;DR

This paper applies a Monte Carlo Renormalization Group method to study entanglement percolation in growing polymer systems, accurately estimating critical exponents and fractal dimensions.

Contribution

It introduces a large cell Monte Carlo Renormalization approach to analyze entanglement percolation in polymer growth models, providing new critical exponent estimates.

Findings

Fractal dimension on 3D lattices matches percolation theory.

Critical exponents are consistent with known percolation values.

Method effectively captures cluster formation in polymer systems.

Abstract

We use a large cell Monte Carlo Renormalization procedure, to compute the critical exponents of a system of growing linear polymers. We simulate the growth of non-intersecting chains in large MC cells. Dense regions where chains get in each others' way, give rise to connected clusters under coarse graining. At each time step, the fraction of occupied bonds is determined in both the original and the coarse grained configurations, and averaged over many realizations. Our results for the fractal dimension on three dimensional lattices are consistent with the percolation value.