Zero-temperature limit of the supersymmetry-breaking complexity in dilute spin-glass models

We study the supersymmetry (SUSY)-breaking complexity of the Bethe lattice spin-glass in the zero temperature limit. We consider both the Gaussian and the bimodal distribution of the coupling constants. For J(ij)=+/- 1 the SUSY breaking theory yields field distributions that concentrate on integer values at low temperatures, at variance with the unbroken SUSY theory. This concentration takes place both in the quenched as well as in the simpler annealed formulation.