The Ising spin glass in a transverse field. Results of two fermionic models

We analyze the long range Ising spin glass in a transverse field by using Grassmann variables in a field theory where the spin operators are represented by bilinear combinations of fermionic fields. We compare the results of two fermionic models. In the four state (4S)-model the diagonal Sz operator has two vanishing eigenvalues, that are suppressed by a restraint in the two states (2S)-model. Within a replica symmetric theory and in the static approximation we obtain similar results for both models.