We argue that non-trivial fixed points bordering on the paramagnetic and ferromagnetic phases are most likely to exist in the Higgs-Yukawa systems that have a connected domain with the paramagnetic phase and no ferrimagnetic phase. We find three examples of such systems; among them is the U(1) system with naive fermions.
@article{arxiv.hep-lat/9411069,
title = {Which Higgs-Yukawa systems can possess non-trivial fixed points},
author = {Sergei V. Zenkin},
journal= {arXiv preprint arXiv:hep-lat/9411069},
year = {2009}
}