Disentangling phase transitions and critical points in the proton–neutron interacting boson model by catastrophe theory

We introduce the basic concepts of catastrophe theory needed to derive analytically the phase diagram of the proton–neutron interacting boson model (IBM-2). Previous studies [1], [2] and [3] were based on numerical solutions. We here explain the whole IBM-2 phase diagram including the precise order of the phase transitions in terms of the cusp catastrophe.