Optimization of Monte Carlo calculations of the effective potential

Abstract

We study Monte Carlo calculations of the effective potential for a scalar field theory using three techniques. In each case we extract the renormalized quantities of the theory. The system studied in our calculations is a one-component φ⁴ model in two dimensions. We apply these methods to both the weak and strong coupling regimes. In the weak coupling regime we compare our results for the renormalized quantities with those obtained from two-loop lattice perturbation theory. Our results are verified in the strong coupling regime through comparison with the strong coupling expansion. We conclude that effective potential methods, when suitably chosen, can be accurate tools in calculations of the renormalized parameters of scalar field theories.