Spinodal and Equilibrium Global Phase Diagram of the d=3 Merged Potts-Cubic-Clock Model: First-Order Equilibrium and Second-Order Spinodal Boundaries with Hidden Topologies from Renormalization-Group Theory

A model that merges the Potts, cubic, and clock models is studied in spatial dimension d=3 by renormalization-group theory. Effective vacancies are included in the renormalization-group initial conditions. In the global phase diagram, 5 different ordered phases, namely ferromagnetic, antiferromagnetic, ferrimagnetic, antiferrimagnetic, axial, and a disordered phase are found, separated by first- and second-order phase boundaries. 8 different phase diagram cross-sections occur. When the effective vacancies are suppressed, the global spinodal phase diagram is found: All disordering phase transitions become second order, the disordered phase recedes, and 17 different phase diagram cross-sections occur, spinodality thus much enriching ordering behavior. In the spinodal phase diagram, the ferrimagnetic and antiferrimagnetic phases have reentrance. The employed renormalization group transformation is exact on the d=3 dimensional hierarchical model and Migdal-Kadanoff approximate on the cubic lattice.