Defect Superdiffusion and Unbinding in a 2D XY Model of Self-Driven Rotors

Area of Science:

• Statistical physics
• Condensed matter theory
• Complex systems

Background:

• The 2D XY model describes systems with XY symmetry and short-range interactions.
• Topological defects, like vortices, are crucial in understanding phase transitions.
• Nonequilibrium systems exhibit unique behaviors not seen in equilibrium.

Purpose of the Study:

• To investigate a nonequilibrium extension of the 2D XY model, equivalent to the noisy Kuramoto model.
• To analyze the impact of self-spinning on topological defects (vortices).
• To understand how self-spinning affects the Berezenskii-Kosterlitz-Thouless phase transition.

Main Methods:

• Studied static and dynamic properties of topological defects (vortices).
• Introduced a nonequilibrium drive with random intrinsic frequencies for rotors on a square lattice.
• Analyzed the resulting phase transition and defect behavior.

Main Results:

• The nonequilibrium drive breaks the quasi-long-range order into controllable-sized ordered domains.
• Self-propelled vortices generically unbind at any temperature.
• Vortices exhibit superdiffusion with ⟨r^{2}(t)⟩∼t^{3/2} and Gaussian displacement distributions.

Conclusions:

• Provides a framework for studying topological defects in nonequilibrium matter.
• Demonstrates how self-spinning alters phase transitions and defect dynamics.
• Offers new insights into the synchronization of locally coupled oscillators.