Monte Carlo simulation of O(2) φ4 field theory in three dimensions -: art. no. 066113

Using standard numerical Monte Carlo lattice methods, we study non-universal properties of the phase transition of three-dimensional phi (4) theory of a two-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 f d(3)x[1/2 \ del phi \ (2) + 1/2r phi (2) + (u/4!) phi (4)]. These values have applications to calculating the phase-transition temperature of dilute or weakly interacting Bose gases (both relativistic and nonrelativistic). 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.