Classical Calculations on the Phase Transition I. Phase Diagram in Four-Dimensional Space for the System with One Order Parameter

As the generalized Landau expression, the star catastrophe potential was investigated. The potential contains four control variables and a behavior variable, which are related to four field variables and one order parameter in physical systems by diffeomorphisms. The phase diagram, structure of critical spaces and coexistence spaces, in four-dimensional space were obtained. New types of singularity named critical coexistence space appear in this potential, which has been introduced by Griffiths as critical end point. In a certain range of the control variables, the triple hysteresis loop was found for this potential with one order parameter.