Microscopic spectral density of the Wilson Dirac operator for one flavor

We consider the effect of a non-zero lattice spacing on the low-energy effective theory of Wilson fermions with Nf=1. Analytical results are given for both the chiral condensate and the microscopic spectral density of the Wilson Dirac operator. It is observed that the partition function for a sector of fixed index ν has ν real zeros. A subtle mechanism ensures that a constant chiral condensate is recovered, once the sum over sectors ν is performed.