Phase Diagram of Strongly Coupled Lattice Yukawa Theories

Using weak and strong Yukawa coupling expansions combined with the mean field theory, we determine the phase structure of Yukawa models with Z</it>(2), O</it>(2), O</it>(4) scalars. We have taken into account all the terms in the relevant expansions up to eighth order. In the leading order, all the Yukawa models have the four phases and do not possess the ferrimagnetic (FI) phase. This feature persists for Z</it>(2) and O</it>(2) Yukawa models to all orders. In the O</it>(4) Yukawa model, on the other hand, the FI phase appears in the next to leading order and all higher orders, and two symmetric phases are completely separated by the FI phase. The result holds irrespective of the choice of fermions; naive or staggered.