Coarse grid Yukawa interaction for staggered fermions

We examine a coarse grid version of the Yukawa coupling between a staggered fermion field χ and a scalar field φ in an attempt to describe the case of four fermion flavors on the lattice. Convincing evidence for the positivity of the fermion determinant is presented. The phase diagram is analyzed by investigating the vacuum expectation value of φ and the chiral condensate of χ by analytical and numerical tools. An expansion up to two-loop order is performed to cover perturbative aspects and an analogy to the Ising model at large Yukawa coupling is explited. In the numerical simulations we mainly rely on the Hybrid Monte Carlo algorithm, although alternatives had to be used because the algorithm in its present form fails to be useful at large Yukawa couplings. Also the issue whether our model is renormalizable at one loop order is discussed. (orig.)