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This study explores a complex spin system, revealing five distinct ordered phases and a disordered phase. These phases are separated by various phase transitions and multicritical points, creating a rich phase diagram.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Many-Body Systems

Background:

  • Understanding complex spin systems is crucial for developing new materials and technologies.
  • Investigating systems with competing interactions, like Potts and clock models, reveals exotic phases and transitions.
  • Renormalization-group techniques are powerful tools for mapping phase diagrams of interacting systems.

Purpose of the Study:

  • To investigate the global phase diagram of a spin system with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions.
  • To identify and characterize the different ordered and disordered phases present in the system.
  • To map the phase transitions and multicritical points bounding these phases in d=2 and d=3 spatial dimensions.

Main Methods:

  • Renormalization-group (RG) solution using the improved Migdal-Kadanoff approximation.
  • Hierarchical lattice models with the inclusion of effective vacancies.
  • Calculation of the global phase diagram for the studied spin system.

Main Results:

  • Identification of five distinct ordered phases: conventionally ordered ferromagnetic, quadrupolar, antiferromagnetic, and algebraically ordered antiferromagnetic, antiquadrupolar phases.
  • Characterization of the disordered phase.
  • Mapping of first- and second-order phase transitions bounding these phases.
  • Identification of various multicritical points, including inverted bicritical, zero-temperature bicritical, tricritical, second-order bifurcation, and zero-temperature highly degenerate multicritical points.

Conclusions:

  • The studied spin system exhibits a rich phase diagram topology with a diverse array of ordered phases and transitions.
  • The interplay between Potts and clock interactions leads to complex emergent phenomena.
  • The employed renormalization-group methods provide a robust framework for understanding such complex systems.