Fermionic Structure of Two-Dimensional Ising Model with Quenched Site Dilution
V. N. Plechko
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.
•Jan 1, 2008•10 citations