Polymer stars in three dimensions. Three loop results

TL;DR

This paper investigates the universal scaling properties of polymer star networks in three dimensions using advanced field theoretical methods, providing three-loop calculations and resummation techniques for critical exponents.

Contribution

It presents the first three-loop renormalization group calculations of star exponents directly in three dimensions for polymer networks with arbitrary topology.

Findings

Calculated critical exponents for polymer star networks.

Applied Pade-Borel and conformal mapping resummation methods.

Provided insights into universal properties of complex polymer structures.

Abstract

We study scaling properties of self avoiding polymer stars and networks of arbitrary given but fixed topology. We use massive field theoretical renormalization group framework to calculate critical exponents governing their universal properties (star exponents). Calculations are performed directly in three dimensions, renormalization group functions are obtained in three loop approximation. Resulting asymptotic series for star exponents are resummed with the help of Pade-Borel and conformal mapping transformation.