Properties of a Two-Dimensional Scalar Field Theory with a $\phi^4$ Interaction*

We investigate properties of a two-dimensional scalar field theory with a $\phi^4$ interaction in the broken phase using the method of Discretized Light-Cone Quantization (DLCQ). Our goal is to extrapolate the critical coupling for vanishing mass gap (with respect to the perturbative vacuum) to infinite longitudinal momentum K in the odd particle sector, the even particle sector, and the degenerate mass of the odd and even sectors of DLCQ. We will present results with both periodic and anti-periodic boundary conditions to elicit effects of neglecting the zero mode in the periodic case.