Fermionic Thouless-Anderson-Palmer equations

We derive the Thouless-Anderson-Palmer (TAP) equations for the fermionic Is ing spin glass. It is found that, just as in the classical Sherrington-Kirk patrick spin-glass model, the conditions for stability and for validity of the free energy are equivalent. We determine the breakdown of the paramagne tic phase. Numerical solutions of the fermionic TAP equations at T = 0 allo wed us to localize a first-order transition between the spin-glass phase an d the paramagnetic phase at mu approximate to 0.8. We computed at zero temp erature the filling factor nu(mu) and the distribution of the internal fiel ds. The saddle-point equations resulting from the calculation of the number of solutions to the TAP equations were found to be much more complicated, as in the classical case.