Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2006-05-22
Nucl. Phys. B 750, 213 (2006)
Physics
Condensed Matter
Disordered Systems and Neural Networks
20 pages, no figures; to appear in Nucl. Phys. B
Scientific paper
10.1016/j.nuclphysb.2006.05.022
We consider a generic time-reversal invariant model of fermions hopping randomly on a square lattice. By means of the conventional replica-trick within the fermionic path-integral formalism, the model is mapped onto a non-linear sigma-model with fields spanning the coset U(4N)/Sp(2N), N->0. We determine the proper scaling combinations of an infinite family of relevant operators which control deviations from perfect two-sublattice symmetry. This allows us to extract the low-energy behavior of the density of states, which agrees with earlier results obtained in particular two-sublattice models with Dirac-like single-particle dispersion. The agreement proves the efficacy of the conventional fermionic-path-integral approach to disordered systems, which, in spite of many controversial aspects, like the zero-replica limit, remains one of the more versatile theoretical tool to deal with disordered electrons.
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