  We apply a new anticommuting path integral technique to clarify the fermionic
structure of the 2D Ising model with quenched site dilution. In the $N$-replica
scheme, the model is explicitly reformulated as a theory of interacting
fermions on a lattice. An unusual feature is that the leading term of
interaction in the exact lattice theory is of order $2N$ in fermions, where $N$
is the number of replicas. The continuum-limit approximation near $T_c $ for
weak dilution produces, however, an effective four-fermion interaction. In
particular, this implies the doubled-logarithmic singularity in the specific
heat near $T_c$ for weak site dilution. The exact value of the initial slope is
also obtained.
  Keywords: Ising model, site disorder, anticommuting Grassmann variables
