Investigations in 1+1 dimensional lattice φ4 theory -: art. no. 094503

In this work we perform a detailed numerical analysis of (1+1) dimensional lattice phi(4) theory. We explore the phase diagram of the theory with two different parametrizations. 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 <phi(R)> does not scale in 1+1 dimensions. We also calculate the renormalized coupling constant lambda(R) in the broken symmetry phase. The ratio lambda(R)/m(R)(2) does not scale and appears to reach a value independent of the bare parameters in the critical region in the infinite volume limit.