Effect of a transverse field on the spin glass freezing in the Sherrington-Kirkpatrick model

Abstract

In the Sherrington-Kirkpatrick (SK) model the effect of a transverse field Delta on the spin glass freezing is studied on the basis of the theory of Thouless, Anderson and Palmer (1977). It is shown from the logarithmic singular point of the free energy in the high-temperature region that Tc decreases with increasing Delta . To be consistent with this result the mean-field equation is set up for T<Tc. Due to the correlation effect spin flips associated with the transverse field are unlikely to occur at low temperatures and the system eventually undergoes the spin glass transition irrespective of the magnitude of Delta , which is characteristic of the SK model.