Continuously Varying Exponents for Oriented Self-Avoiding Walks

Abstract

A two-dimensional conformal field theory with a conserved $U(1)$ current $\vec J$, when perturbed by the operator ${\vec J}^{\,2}$, exhibits a line of fixed points along which the scaling dimensions of the operators with non-zero $U(1)$ charge vary continuously. This result is applied to the problem of oriented polymers (self-avoiding walks) in which the short-range repulsive interactions between two segments depend on their relative orientation. While the exponent $ν$ describing the fractal dimension of such walks remains fixed, the exponent $γ$, which gives the total number $\sim N^{γ-1}μ^N$ of such walks, is predicted to vary continuously with the energy difference.