Microcanonical phase diagram of the BEG and Ising models

The density of states of long-range Blume - Emery - Griffiths (BEG) and short-range Ising models are obtained by using Wang - Landau sampling with adaptive windows in energy and magnetization space. With accurate density of states, we are able to calculate the microcanonical specific heat of fixed magnetization introduced by Kastner et al. in the regions of positive and negative temperature. The microcanonical phase diagram of the Ising model shows a continuous phase transition at a negative temperature in energy and magnetization plane. However the phase diagram of the long-range model constructed by peaks of the microcanonical specific heat looks obviously different from the Ising chart.