Critical properties of a generalized pseudospin Hamiltonian

Abstract

A two-parameter pseudospin Hamiltonian is introduced which contains both the Meshkov-Glick-Lipkin and the Abecasis-F\"assler-Plastino Hamiltonians as special cases. The ground state critical properties of the two-parameter Hamiltonian are determined: It exhibits both first and second order phase transitions. The ground state critical properties of any one-parameter pseudospin Hamiltonian contained in the two-parameter model can immediately be determined by inspecting the interaction parameter space of the two-parameter model. The critical set in this space is identified with that of the cusp catastrophe.NUCLEAR STRUCTURE Pseudospin Hamiltonian, critical properties, first and second order phase transitions.