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 $\nu$ describing the fractal dimension of such walks remains fixed, the exponent $\gamma$, which gives the total number $\sim N^{\gamma -1}{\mu }^N$ of such walks, is predicted to vary continuously with the energy difference.

15 pages, plain TeX, 2 uuencoded postscript figures, OUTP-93-41S

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