  Using standard numerical Monte Carlo lattice methods, we study non-universal
properties of the phase transition of three-dimensional phi^4 theory of a
2-component real field phi = (phi_1,phi_2) with O(2) symmetry. Specifically, we
extract the renormalized values of <phi^2>/u and r/u^2 at the phase transition,
where the continuum action of the theory is \int d^3x [ (1/2) |\grad\phi|^2 +
\half r \phi^2 + {u\over4!} \phi^4 ]. These values have applications to
calculating the phase transition temperature of dilute or weakly-interacting
Bose gases (both relativistic and non-relativistic). In passing, we also
provide perturbative calculations of various O(a) lattice-spacing errors in
three-dimensional O(N) scalar field theory, where (a) is the lattice spacing.
