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Merged Potts-clock model: Algebraic and conventional multistructured multicritical orderings in two and three
E Can Artun1,2, A Nihat Berker1,2,3
1TÜBITAK Research Institute for Fundamental Sciences, Gebze, Kocaeli 41470, Turkey.
Physical Review. E
|September 19, 2023
Summary
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.
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.
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