Directed Polymer Blends and Quantum Critical Phenomena

Abstract

The statistical mechanics of directed line-like objects, such as directed polymers in an external field, strands of dipoles in both ferro- and electrorheological fluids, and flux lines in high-$T_{\tiny C}$ superconductors bears a close resemblance to the quantum mechanics of bosons in $2+1$ dimensions. We show that single component and binary mixture critical phenomena in these systems are in the universality class of three dimensional uniaxial dipolar ferromagnets and ferroelectrics. Our results also apply to films of two superfluid species undergoing phase separation well below their $λ$-points near $T=0$. In the case of directed polymers and electrorheological fluids we analyze the effects of free ends occurring in the sample as well as a novel directionally-dependent compressibility.