Flory theory for directed lattice animals and directed percolation

The free energies of directed lattice animals in good and theta -solvents, and the free energy of directed percolation are found by the use of a simple Flory-type approximation, which accounts for the inherent anisotropy of these systems. From these free energies, the authors obtain the upper critical dimension below which mean-field theory breaks down. They also calculate closed-form, dimension-dependent expressions for the parallel and perpendicular correlation length exponents, which characterise the asymptotic cluster shapes. These exponents are in excellent agreement with existing numerical data.