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Updated: Sep 19, 2025
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
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Phase transitions in the q-state clock model
Arpita Goswami1, Ravi Kumar1, Monikana Gope1
1Indian Institute of Technology, Tirupati 517619, India.
Physical Review. E
|June 19, 2025
Summary
The q-state clock model exhibits three distinct phases for large q, with transitions characterized by mean-field theory. Lower temperature transitions show characteristics of large-order symmetry breaking, while higher temperature transitions are Berezinskii-Kosterlitz-Thouless (BKT) type.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Phase Transitions
Background:
- The q-state clock model, a discrete XY model, displays second-order phase transitions for q≤4 in 2D.
- The q→∞ limit corresponds to the XY model, exhibiting an infinite-order Berezinskii-Kosterlitz-Thouless (BKT) transition.
Purpose of the Study:
- To systematically investigate the q-state clock model for q≥5 using mean-field (MF) theories.
- To clarify the nature of the three predicted phases and two associated phase transitions.
Main Methods:
- Development of basic and higher-order mean-field (MF) theories.
- Systematic calculations to analyze the model's thermodynamic phases and transitions.
Main Results:
- Reaffirmation of three phases for large q: Z_q symmetric ferromagnetic (low T), emergent U(1) symmetric BKT (intermediate T), and paramagnetic (high T).
- The higher temperature transition is identified as BKT type.
- The lower temperature transition is characterized as large-order spontaneous symmetry breaking, potentially mimicking BKT characteristics.
Conclusions:
- Higher-order MF theory provides improved phase characterization by estimating spin-spin correlations.
- The study elucidates the complex phase diagram and transition behaviors of the 2D q-state clock model for large q.
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