Short-Range Berezinskii-Kosterlitz-Thouless Phase Characterization for the q-State Clock Model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Information Theory

Background:

• Spin systems commonly exhibit ferromagnetic and paramagnetic phases.
• The q-state clock model, for q ≥ 5, displays an intermediate vortex state.
• This vortex state leads to the Berezinskii-Kosterlitz-Thouless (BKT) phase, observed up to the XY model (q→∞).

Purpose of the Study:

• To analyze classical order parameters and introduce novel short-range parameters for spin systems.
• To investigate the distinguishability of transitions in the q-state clock model using information theory.
• To determine the role of short-range interactions in the appearance and disappearance of the BKT phase.

Main Methods:

• Application of information theory to analyze spin system parameters.
• Definition and utilization of new short-range parameters.
• Analysis of first nearest neighbors spin-spin correlations.

Main Results:

• Successfully distinguished the two transitions in the q-state clock model (q ≥ 5) using only first nearest neighbors spin-spin correlations.
• Demonstrated that information content from classical and new parameters uniquely identifies the BKT phase's temperature-dependent behavior.
• Showcased the critical role of short-range interactions in the onset and termination of the BKT phase.

Conclusions:

• Information-theoretic analysis of short-range correlations provides a robust method for characterizing phase transitions in spin systems.
• The study elucidates the fundamental role of local interactions in the emergence and dissolution of complex phases like the BKT phase.
• This approach offers a powerful tool for understanding critical phenomena in diverse physical systems beyond the q-state clock model.