We consider the classical time evolution of a real scalar field in two-dimensional Minkowski space with a [Formula: see text] interaction. We compute the spatial and temporal two-point correlation functions and extract the renormalized mass of the interacting theory. We find our results are consistent with the one- and two-loop quantum computation. We also perform Monte Carlo simulations of the quantum theory and conclude that the classical scheme is able to produce more accurate results with a fraction of the CPU time. PACS Nos.: 03.70.+k, 03.50.–z, 11.15.Tk