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Partition function zeros of the p-state clock model in the complex temperature plane.

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Summary

This study uses the Wang-Landau method to analyze partition function zeros in the 2D p-state clock model. Results confirm the upper transition at p=6 is Berezinskii-Kosterlitz-Thouless (BKT) type, challenging prior claims.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Phase transitions

Background:

  • The two-dimensional p-state clock model exhibits complex phase behavior.
  • Understanding phase transitions, particularly the Berezinskii-Kosterlitz-Thouless (BKT) type, is crucial in statistical physics.
  • Partition function zeros provide insights into critical phenomena and phase transition types.

Purpose of the Study:

  • To investigate the nature of the upper phase transition in the 2D p-state clock model.
  • To determine if the transition at p=6 is of the BKT type using partition function zeros.
  • To compare the behavior of partition function zeros for different values of p.

Main Methods:

  • Utilizing the Wang-Landau method for density of states calculation.
  • Employing a modified energy representation to avoid binning artifacts in energy level enumeration.
  • Analyzing the location and behavior of partition function zeros in the complex temperature plane.

Main Results:

  • Strong evidence suggests the upper transition at p=6 is BKT type, contradicting previous Fisher zero studies.
  • Leading zeros for p=6 align with larger p values and the XY model, unlike the finite-size behavior of p=5.
  • The small partition function magnitude near the BKT transition limits the system sizes accessible for zero analysis.

Conclusions:

  • The upper transition in the 2D p-state clock model at p=6 is confirmed as BKT type.
  • The finite-size scaling of partition function zeros differs for p=5 compared to p≥6.
  • The characteristics of the BKT transition, including nondivergent specific heat, inherently limit the study of its zeros in large systems.