A perturbation expansion for the Sherrington-Kirkpatrick model with a transverse field

In the Sherrington-Kirkpatrick model the effect of a transverse field Delta on spin glass freezing is studied. After the static approximation of the replica theory has been analysed, the nonlinear susceptibility is calculated by the perturbation method with respect to exchange coupling Jij up to the tenth order. The freezing temperature and the critical index of the nonlinear susceptibility are evaluated. The result shows that the system remains paramagnetic for Delta >1.506 J (the variance of (Jij) is J2/N), which corrects the conjecture made before by the present authors. It is also shown that the static approximation in the replica theory overestimates Tc for a large value of Delta .