Does the 2d Higgs-Yukawa Model Have a Symmetric Phase at Small Yukawa Coupling Region?

TL;DR

This paper demonstrates that the 2d Higgs-Yukawa model with Z(2) symmetry remains in a broken phase at small Yukawa couplings and is asymptotically free, confirming recent numerical conjectures.

Contribution

It provides an analytical proof that the model stays in the broken phase at small Yukawa coupling and is asymptotically free, supporting recent numerical findings.

Findings

Model remains in broken phase at small Yukawa coupling

Model is asymptotically free as cutoff increases

Results agree with recent numerical simulations

Abstract

We show that at arbitrary value of the scalar self coupling and small Yukawa coupling $y$ the 2d Higgs-Yukawa model with Z(2) symmetry remains in the broken phase and the model is asymptotically free: $y \to 0$ as the cut-off $\Lambda \to \infty$. This is in agreement with a recent conjecture based on numerical simulation results.