In this work we perform a detailed numerical analysis of (1+1) dimensional lattice φ 4 theory. We explore the phase diagram of the theory with two different parameterizations. We find that symmetry breaking occurs only with a negative mass-squared term in the Hamiltonian. The renormalized mass m R and the field renormalization constant Z are calculated from both coordinate space and momentum space propagators in the broken symmetry phase. The critical coupling for the phase transition and the critical exponents associated with m R , Z and the order parameter are extracted using a finite size scaling analysis of the data for several volumes. The scaling behavior of Z has the interesting consequence that φ R does not scale in 1 + 1 dimensions. We also calculate the renormalized coupling constant λ R in the broken symmetry phase.The ratio λ R /m 2 R does not scale and appears to reach a value independent of the bare parameters in the critical region in the infinite volume limit.

We investigate the continuum limit of a compact formulation of the lattice U(1) gauge theory in 4 dimensions using a nonperturbative gauge-fixed regularization. We find clear evidence of a continuous phase transition in the pure gauge theory for all values of the gauge coupling (with gauge symmetry restored). When probed with quenched staggered fermions with U(1) charge, the theory clearly has a chiral transition for large gauge couplings. We identify the only possible region in the parameter space where a continuum limit with nonperturbative physics may appear.Comment: latex, 9 pages, 7 figures. Version accepted for publication in Phys. Lett.

We investigate the topological charge in 1 1 dimensional 4 theory on a lattice with antiperiodic boundary condition (APBC) in the spatial direction. We propose a simple order parameter for the lattice theory with APBC and we demonstrate its effectiveness. Our study suggests that kink condensation is a possible mechanism for the order-disorder phase transition in the 1 1 dimensional 4 theory. With renormalizations performed on the lattice with periodic boundary condition (PBC), the topological charge in the renormalized theory is given as the ratio of the order parameters in the lattices with APBC and PBC. We present a comparison of topological charges in the bare and the renormalized theory and demonstrate invariance of the charge of the renormalized theory in the broken symmetry phase.

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