Artun, E. CanBerker, A. Nihat2023-10-192023-10-19202302470-00452470-0053https://doi.org/10.1103/PhysRevE.108.024116https://hdl.handle.net/20.500.12469/5078A spin system is studied with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions in spatial dimensions d = 2 and 3. The global phase diagram is calculated from the renormalization-group solution with the recently improved (spontaneous first-order detecting) Migdal-Kadanoff approximation or, equivalently, with hierarchical lattices with the inclusion of effective vacancies. Five different ordered phases are found: Conventionally ordered ferromagnetic, quadrupolar, antiferromagnetic phases and algebraically ordered antiferromagnetic, antiquadrupolar phases. These five different ordered phases and the disordered phase are mutually bounded by first-and second-order phase transitions, themselves delimited by multicritical points: Inverted bicritical, zero-temperature bicritical, tricritical, second-order bifurcation, and zero-temperature highly degenerate multicritical points. One rich phase diagram topology exhibits all of these phenomena.eninfo:eu-repo/semantics/openAccess2nd-Order Phase-TransitionsRenormalization-GroupHierarchical LatticesSpin Systems1st-Order2nd-Order Phase-TransitionsRenormalization-GroupHierarchical LatticesSpin Systems1st-OrderArticle2108WOS:00105311170000110.1103/PhysRevE.108.0241162-s2.0-85167997029Q1Q137723754