  Histogram-reweighting Monte Carlo simulations were used to obtain polymer /
solvent phase diagrams for lattice homopolymers of chain lengths up to r=1000
monomers. The simulation technique was based on performing a series of grand
canonical Monte Carlo calculations for a small number of state points and
combining the results to obtain the phase behavior of a system over a range of
temperatures and densities. Critical parameters were determined from
mixed-field finite-size scaling concepts by matching the order parameter
distribution near the critical point to the distribution for the
three-dimensional Ising universality class. Calculations for the simple cubic
lattice (coordination number z=6) and for a high coordination number version of
the same lattice (z=26) were performed for chain lengths significantly longer
than in previous simulation studies. The critical temperature was found to
scale with chain length following the Flory-Huggins functional form. For the
z=6 lattice, the extrapolated infinite chain length critical temperature is
3.70+-0.01, in excellent agreement with previous calculations of the
temperature at which the osmotic second virial coefficient is zero and the mean
end-to-end distance proportional to the number of bonds. This confirms that the
three alternative definitions of the Theta-temperature are equivalent in the
limit of long chains. The critical volume fraction scales with chain length
with an exponent equal to 0.38+-0.01, in agreement with experimental data but
in disagreement with polymer solution theories. The width of the coexistence
curve prefactor was tentatively found to scale with chain length with an
exponent of 0.20+-0.03 for z = 6 and 0.22+-0.03 for z = 26. These values are
near the lower range of values obtained from experimental data.
