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 Tc for weak dilution produces, however, an effective four-fermion interaction. In particular, this implies the doubled-logarithmic singularity in the specific heat near Tc for weak site dilution. The exact value of the initial slope is also obtained.
The notion of the integral over the anticommuting Grassmann variables is applied to analyze 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. For weak dilution, the continuum-limit approximation implies the log-log singularity in the specific heat near
Tc.