Instabilities and replica-symmetry breaking in the four-state clock spin glass

Abstract

The infinite-range four-state clock spin glass, in the presence of an arbitrary magnetic field, is investigated by the replica method. The appropriate replica-symmetry breaking scheme is discussed for this model. It is shown that two distinct Almeida-Thouless lines are possible, depending on the direction of the applied field. The full phase diagram of the model, showing its instability regions, is presented and discussed.