DIRECTION DIRECTION CORRELATIONS OF ORIENTED POLYMERS

We calculate the direction-direction correlations between the tangent vectors of an oriented self-avoiding walk (SAW). Let J-mu-(x) and J(v)(0) be components of unit-length tangent vectors of an oriented SAW, at the spatial points x and 0, respectively. Then for distances \x\ much less than the average distance between the endpoints of the walk, the correlation function of J-mu-(x) with J(v)(0) has, in d dimensions, the form <J-mu-(x) J(v)(0)> = k(d)(x-mu-x(v) - 1/2x2-delta-mu-v)/\x\2d. The dimensionless amplitude k(d) is universal, and can be calculated exactly in two dimensions by using Coulomb gas techniques, where it is found to be k(2) = 12/25-pi-2. In three dimensions, the epsilon-expansion to second order in epsilon together with the exact value of k(2) in two dimensions allows the estimate k(3) = 0.0178 +/- 0.0005. In dimensions d greater-than-or-equal-to 4, the universal amplitude k(d) of the direction-direction correlation functions of an oriented SAW is the same as the universal amplitude of the direction-direction correlation functions of an oriented random walk, and is given by k(d) = GAMMA-2(d/2)/(d - 2)pi-d.