Topological Constraints at the Theta Point: Closed Loops at Two Loops

William Kung, Randall D. Kamien

Published 2003-05-01, updated 2003-05-09Version 2

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe, which gives way to a fluctuation-induced first-order transition.