On the relevance of percolation theory to the vulcanization transition

Abstract

The relationship between vulcanization and percolation is explored from the perspective of renormalized local field theory. We show rigorously that the vulcanization and percolation correlation functions are governed by the same Gell--Mann-Low renormalization group equation. Hence, all scaling aspects of the vulcanization transition are reigned by the critical exponents of the percolation universality class.