Flory approximation for directed branched polymers and directed percolation

The Flory approximation for the radius of gyration of dilute polymers is generalized to systems with a preferred direction. The mean radius then increases with their size N as Nν∥ in the preferred direction and as Nν〉 in the transverse directions. In the case of directed branched polymers (lattice animals) and of directed percolation, the upper critical dimension dc is predicted correctly, and the values obtained by ν∥ and ν 〉 are in very good agreement with the values from other methods in dimensions 2 and 3. An expansion in (dc - d) shows that the results are not exact in general, as is the case for unoriented polymers.