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, separated by tricritical points. When the effective vacancies are suppressed, the global spinodal phase diagram is found: All disordering phase transitions become second order, the disordered phase recedes revealing hidden topologies, spinodality thus much enriching ordering behavior. 50 different phase diagram cross-sections are calculated. The employed renormalization group transformation is exact on the d=3 dimensional hierarchical model and Migdal–Kadanoff approximate on the cubic lattice.