Investigations in 1+1 dimensional lattice ${\varphi }^4$ theory

Abstract

In this work we perform a detailed numerical analysis of (1+1) dimensional lattice ${\varphi }^4$ 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 $<{\varphi }_R>$ 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.

RevTex, 26 pages, 20 eps figures, revised version

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Cited by in corpus (8)

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• Effects of boundary conditions and gradient flow in 1+1 dimensional lattice ${\varphi }^4$ theory
• Topological charge in 1+1 dimensional lattice ${\varphi }^4$ theory
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model
• Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory