Yunus, Ç.Renklioǧlu, B.Keskin, M.Berker, A. N.2018-04-122018-04-1220162470-0045http://hdl.handle.net/11693/36539The spin-32 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.EnglishChemical potentialGroup theoryIsing modelLattice theoryStatistical mechanicsDouble critical pointGlobal phase diagramsMigdal-Kadanoff approximationNearest-neighbor interactionsOrientational orderingsRenormalization groupRenormalization group theoryTetracritical pointsPhase diagramsArticle10.1103/PhysRevE.93.062113