POLYMERS WITH LONG-RANGED SELF-REPULSION - A VARIATIONAL APPROACH

We use a variational approach to study self interacting polymers with long-ranged repulsion decaying for large distances as r-lambda. For 2 less-than-or-equal-to lambda less-than-or-equal-to 4 and lambda < d (where d is the spatial dimension), we find that the exponent for the end-to-end distance of the chain is nu = 2/lambda (with logarithmic corrections for lambda = 2 or lambda = 4), in agreement with renormalization group computations and recent numerical simulations. We discuss the entire lambda, d plane, using a renormalization group near lambda = 4, d = 4.