Phase diagram of a lattice SU(2) x SU(2) scalar-fermion model with naive and Wilson fermions

We present the phase structure of the chiral SU(2)L x SU(2)R scalar-fermion model on the lattice with on-site Yukawa coupling y and Wilson-Yukawa coupling w for positive y and w. The hopping parameter κ of the four-component scalar field of fixed length is both positive and negative. From the different behaviour of several observables ferromagnetic, paramagnetic and antiferromagnetic phases can be distinguished. They split into different regions or phases with small and large y+4w. A similar structure is also found in the quenched approximation. In addition, in the unquenched case a ferrimagnetic phase is found at negative κ around y+4w ≅ √2. We discuss fermion masses in various regions and point out the possibilities of decoupling the unwanted fermion doublers in the continuum limit in analogy to the Wilson mechanism. (orig.)