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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.

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|June 19, 2025
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Summary
This summary is machine-generated.

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.

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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.