On a mean field approximation for Higgs-Yukawa systems

TL;DR

This paper investigates the phase structure of lattice Higgs-Yukawa systems using a mean field approximation, revealing artifacts and dimensional effects on phase diagrams.

Contribution

It introduces a variational mean field approach with fermionic determinant contributions in a ladder approximation for Higgs-Yukawa systems.

Findings

Ferrimagnetic phase can be an artifact of finite lattice size.

Phase diagram changes qualitatively at four dimensions.

Dimensional effects influence phase structure in the model.

Abstract

We discuss the phase structure of a lattice Higgs-Yukawa system in the variational mean field approximation with contributions of fermionic determinant being calculated in a ladder approximation. In particular, we demonstrate that in this approximation the ferrimagnetic phase in the $Z_2$ model with naive fermions can appear as an artifact of a finite lattice and that the phase diagram for this model on infinite lattice changes qualitatively at space-time dimension $D = 4$ compared with those at $D > 4$.