Investigations in 1+1 dimensional lattice ϕ⁴ theory

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In this work we perform a detailed numerical analysis of (1+1) dimensional lattice ϕ⁴ 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 mᵣ 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 mᵣ, 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 <ϕᵣ> does not scale in 1+1 dimensions. We also calculate the renormalized coupling constant λᵣ in the broken symmetry phase. The ratio λᵣ/mᵣ² does not scale and appears to reach a value independent of the bare parameters in the critical region in the infinite volume limit.