  Flory-Huggins theory is a mean field theory for modelling the free energy of
dense polymer solutions and polymer melts. In this paper we use Flory-Huggins
theory as a model of a dense two dimensional self-avoiding walk confined to a
square in the square lattice. The theory describes the free energy of the walk
well, and we estimate the Flory interaction parameter of the walk to be
$\chi_{saw} = 0.32(1)$.
