Spontaneous symmetry breaking on the lattice generated by Yukawa interaction

TL;DR

This paper investigates the behavior of a lattice Yukawa model with weakly ferromagnetic or antiferromagnetic scalar interactions, analyzing the scalar propagators and renormalized Yukawa coupling to assess the possibility of a nontrivial fixed point.

Contribution

The study introduces methods for analyzing complex scalar propagators influenced by fermion loops and phase proximity, providing insights into the fixed point structure of the Yukawa model.

Findings

Yukawa coupling reaches its maximum in the studied region.

Scalar field renormalization constant becomes small at negative 7.

No evidence of a nontrivial fixed point due to unitarity bound constraints.

Abstract

We study by numerical simulation a lattice Yukawa model with naive fermions at intermediate values of the Yukawa coupling $y$ when the nearest neighbour coupling $\kp$ of the scalar field $\Phi$ is very weakly ferromagnetic ($\kp \approx 0$) or even antiferromagnetic ($\kappa < 0$) and the nonvanishing value of $\vev$ is generated by the Yukawa interaction. The renormalized Yukawa coupling $y_R$ achieves here its maximal value and this $y$-region is thus of particular importance for lattice investigations of strong Yukawa interaction. However, here the scalar field propagators have a very complex structure caused by fermion loop corrections and by the proximity of phases with antiferromagnetic properties. We develop methods for analyzing these propagators and for extracting the physical observables. We find that going into the negative $\kp$ region, the scalar field renormalization constant becomes small and $y_R$ does not seem to exceed the unitarity bound, making the existence of a nontrivial fixed point in the investigated Yukawa model quite unlikely.