Ordering and Defect Cloaking in Nonreciprocal Lattice XY Models

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• The nonreciprocal planar spin model is crucial for understanding collective behavior in various physical systems.
• Previous studies, like Toner-Tu, established universality classes for similar models.
• Lattice structure and anisotropy are known to influence emergent phenomena in spin systems.

Purpose of the Study:

• To analytically and numerically investigate the nonreciprocal planar spin model on square and triangular lattices.
• To determine the impact of lattice anisotropy on the model's large-scale behavior and universality class.
• To analyze the dynamics and interactions of topological defects within the model's polar-ordered phase.

Main Methods:

• Analytical examination of the spin model's properties.
• Numerical simulations on square and triangular lattices.
• Analysis of long-wavelength equal-time correlators.
• Investigation of topological defect interactions and their impact on phase stability.

Main Results:

• Lattice anisotropy induces a "mass" for the spin angle field, deviating from the Toner-Tu universality class.
• Evidence of this mass is found numerically for large nonreciprocity parameters.
• Anisotropic defect interactions were observed, shielding ±1 defect pairs and delaying annihilation.
• This leads to the destruction of the polarized phase via an
• aster apocalypse,
• similar to findings in flocking models.

Conclusions:

• The nonreciprocal planar spin model exhibits unique behavior driven by lattice anisotropy, not conforming to established universality classes.
• Topological defect dynamics play a critical role in phase transitions, leading to novel pattern formation.
• The findings suggest a broader applicability of these concepts to systems with anisotropic interactions and defect-mediated phase transitions.