Symmetry-breaking in the Lipkin model

Generalized version of the standard Lipkin model is presented. Parity-breaking is studied in both standard and generalized Lipkin models. The generalized Lipkin model Hamiltonian is derived from an octupole-octupole Hamiltonian. It is shown that only the generalized Lipkin model gives asymptotic zero energy splitting between the first positive and the first negative parity states for both even and odd numbers of particles as one expects in the case of octupole deformation.