Competing nematic interactions in a generalized XY model in two and three dimensions

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The XY model is a fundamental model in statistical mechanics.
• Understanding phase transitions is crucial in condensed matter physics.
• Generalizations of the XY model reveal richer physical phenomena.

Purpose of the Study:

• To investigate a generalized XY model with an additional nematic-like term.
• To explore the phase diagram of this model, focusing on the q=8 case.
• To identify and characterize novel phase transitions beyond the standard Berezinskii-Kosterlitz-Thouless (BKT) type.

Main Methods:

• Extensive numerical simulations.
• Finite-size scaling techniques.
• Analysis of two and three-dimensional systems.

Main Results:

• The generalized model exhibits a richer phase diagram than the standard XY model (q=2).
• New infinite-order transitions involving intermediate, competition-driven phases were discovered for q=8.
• Results indicate that vortex decoupling alone is insufficient to classify a transition as BKT type.

Conclusions:

• The generalized XY model with a nematic term presents complex critical behavior.
• The study identifies novel phase transitions and phases not present in simpler models.
• The findings refine the criteria for identifying BKT-type transitions.