Multicritical Points in a Lattice Yukawa Model with the Wilson-Yukawa   Coupling
  For a lattice regularized chiral-invariant $SU(2)_L\times~SU(2)_R$ fermion-scalar model with a Yukawa coupling $y$ and a Wilson-Yukawa coupling $w$, we investigate the phase structure and in particular show the existence of the multicritical line, in the strong Yukawa and/or Wilson Yukawa coupling region, at which four phases meet.   The result is in good agreement with the Monte Carlo simulation.   This analytical result is derived from the effective scalar model obtained by integrating out the fermion field where the action is explicitly obtained from the hopping parameter expansion up to next-to-leading order.   For estimates on the correlation function of the scalar field we apply the mean-field method. 
T. Ebihara and K.-I. Kondo