Replica symmetry breaking of the Ising spin glass in the Bethe and cluster approximations

The Ising spin glass model in a magnetic field is studied within the Bethe and a related cluster approximations. Using replicas, spin glass order parameter function and the de Almeida-Thouless (AT) line are obtained close to the spin glass transition temperature. The results for the Bethe approximation deviate considerably from those for the Sherrington-Kirkpatrick (SK) model.