Europhys. Lett.
Volume 64, Number 3, November 2003
Page(s) 323 - 329
Section Atomic and molecular physics
Published online 01 November 2003
DOI: 10.1209/epl/i2003-00177-6
Europhys. Lett., 64 (3) , pp. 323-329 (2003)

Topological constraints at the Theta-point: Closed loops at two loops

W. Kung and R. D. Kamien

Department of Physics and Astronomy, University of Pennsylvania Philadelphia, PA 19104-6396, USA

(Received 2 May 2003; accepted in final form 29 August 2003)

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 $N\rightarrow 0$. 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.

36.20.-r - Macromolecules and polymer molecules.
64.60.Fr - Equilibrium properties near critical points, critical exponents.
11.15.-q - Gauge field theories.

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