Correlations near the vulcanization transition: A renormalization-group approach

TL;DR

This paper develops a renormalization-group framework to analyze correlators at the vulcanization transition, revealing critical exponents and their relation to percolation theory, with insights into two-dimensional behavior.

Contribution

It introduces a minimal model incorporating thermal motion and quenched constraints, and computes critical exponents near six dimensions for the vulcanization transition.

Findings

Critical exponents match those in percolation theory.

Correlators are constructed and analyzed via RG approach.

Insights into two-dimensional vulcanization transition are discussed.

Abstract

Correlators describing the vulcanization transition are constructed and explored via a renormalization group approach. This approach is based on a minimal model that accounts for the thermal motion of constituents and the quenched random constraints imposed on their motion by crosslinks. Critical exponents associated with the correlators are obtained near six dimensions, and found to equal those governing analogous entities in percolation theory. Some expectations for how the vulcanization transition is realized in two dimensions, developed with H. E. Castillo, are discussed.