Emergent Physics at the Vulcanization Transition

The Essay starts with an overview of the percolation approach and classical elasticity theory of the vulcanization transition of rubber, describing their assumptions and their limitations. Thereafter we discuss a third approach, the Vulcanization Theory (VT) which incorporates the effects of thermal fluctuations and quenched random disorder. The VT is an order parameter theory in the true Landau tradition. We discuss the very subtle type of spontaneous symmetry breaking that occurs in the transition from liquids to amorphous solids and we define a suitable order parameter that captures this symmetry breaking. This necessitates the introduction of replica field theory, and we discuss what these replicas represent physically. We also discuss the physical meaning behind the resulting Goldstone modes. We conclude the Essay by describing a few applications of VT.