Fermionic Structure of Two-Dimensional Ising Model with Quenched Site Dilution

Details Fermionic Structure of Two-Dimensional Ising Model with Quenched Site Dilution Fermionic Structure of Two-Dimensional Ising Model with Quenched Site Dilution

1997-11-24

arxiv.org/abs/cond-mat/9711247v2

Phys. Lett. A 239 (1998) 289-299

Physics

Condensed Matter

Disordered Systems and Neural Networks

LaTeX, 1 + 14 pages, no figures

Scientific paper

10.1016/S0375-9601(98)00022-X

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

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