Replica symmetry breaking in the transverse-field Ising spin-glass model : two fermionic representations

Abstract

We analyze the infinite range Ising spin glass in a transverse-field below the critical temperature by a one step replica symmetry breaking theory. The set of n replicas is divided in r blocks of m replicas each. We present results for different values of the block-size parameter m. The spin operators are represented by bilinear combinations of fermionic fields and we compare the results of two models: In the four-states 4-S model the diagonal Si z operator has two unphysical vanishing eigenvalues, that are suppressed by a restraint in the two-states 2-S model. In the static approximation we obtain qualitatively similar results for both models. They both exhibit a critical temperature Tc that decreases when increases, until it reaches a quantum critical point at the same value of c and they are both unstable under replica symmetry breaking in the whole spin glass phase. Below the critical temperature we present results for the order parameters and free energy.