Ghatak-Sherrington Model with SpinS

Abstract

We investigate the Ghatak-Sherrington model with S ≥1, including S =∞, in a framework of the replica method, namely in terms of the replica symmetry (RS) solutions, the de Almeida and Thouless (AT) stability analysis and the one-step replica symmetry breaking (RSB) solutions. We find that there is a first order transition of van der Waals type between the paramagnetic phase and the spin glass phase and also a first order transition between the RS solution and the RSB solution in the model with integral S in some range of anisotropy parameter, while there is only a continuous transition in the model with half-integral S , including S =∞. We find that the model with integral S has a critical end point under the external magnetic field. We obtain phase diagrams as for the AT stability for the model under the external magnetic field.