Direction-direction correlations of oriented polymers

We calculate the direction-direction correlations between the tangent vectors of an oriented self-avoiding walk (SAW). LetJ (x) andJ ^v (0) be components of unit-length tangent vectors of an oriented SAW, at the spatial pointsx and 0, respectively. Then for distances |x| much less than the average distance between the endpoints of the walk, the correlation function ofJ (x) withJ ^v (0) has, ind dimensions, the form . The dimensionless amplitudek(d) is universal, and can be calculated exactly in two dimensions by using Coulomb gas techniques, where it is found to bek(2)=12/25 ². In three dimensions, the -expansion to second order in together with the exact value ofk(2)in two dimensions allows the estimatek(3)=0.0178±0.0005. In dimensionsd4, the universal amplitudek(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 byk(d)= ²(d/2)/(d–2) ^d .