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Bethe Lattice Spin Glasses (BLSG) are models with finite connectivity whichundergo a Replica Symmetry Breaking (RSB) phase transition in field, even atzero temperature. The order parameter describing this phase is a functionrelated to the non-trivial organization of the states. We compute numericallythe spin glass order parameter at zero temperature in BLSG with coordinationnumber $z=3$ and couplings $J=\pm1$, near the transition. The method is basedon a universal formula which relates the order parameter to the jointprobability distribution of the energy gaps of the lowest lying states. Suchdistribution is derived numerically by introducing a convenient bulkperturbation to the Hamiltonian.

Computation of the Zero Temperature RSB parameter in Bethe Lattice Spin Glasses