Fermionic Path Integrals and Two-Dimensional Ising Model with Quenched Site Disorder

Abstract

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 $T_c$.

Comments: LaTeX, 5 pages, no figures. A plenary talk at the 6th International Conference on Path Integrals from peV to TeV, August 25--29, 1998, Florence, Italy