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

Abstract

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.