Monte Carlo simulation of O(2) phi^4 field theory in three dimensions

Abstract

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) |\gradϕ|^2 + \half r ϕ^2 + {u\over4!} ϕ^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.