Lattice study of a Yukawa theory with a real scalar field

Abstract

Using a combination of analytic mean field techniques and hybrid Monte Carlo simulations, we determine the phase structure of a 4d Yukawa theory with a one-component scalar field interacting with two species of staggered lattice fermions. In a parametrization of the theory in terms of the Yukawa coupling γ and the nearest-neighbor scalar field coupling κ and quartic coupling λ, we find four different phases: (1) symmetric, disordered; (2) ferromagnetic; (3) antiferromagnetic; and (4) simultaneously ferromagnetically and antiferromagnetically ordered. To study the continuum limit of the model, we measure correlation functions and extract masses and renormalized scalar and Yukawa couplings close to the (second-order) phase boundary between phases (1) and (2). The current parametrization allows us to extend significantly previous studies of renormalized couplings and to probe a very large range of bare couplings in continuum parametrization. The renormalized Yukawa coupling γ R is always found to be ⪅1.5 for the range of bare coupling covered. The values of λ R are also bounded and exhibit only weak sensitivity to the bare λ. Comparisons are made with λ R values obtained in the pure 4d λø 4 theory.