Inescapable Anisotropy of Nonreciprocal XY Models

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Active Matter Physics

Background:

• Nonreciprocal XY (NRXY) models introduce position-dependent coupling strengths.
• Previous work established nonreciprocity's link to self-propulsion in similar systems.

Purpose of the Study:

• Investigate the behavior of NRXY models on 2D lattices.
• Characterize the ordered phase and its limitations.

Main Methods:

• Derivation of a mean-field continuous theory.
• Analysis of lattice-induced anisotropy and fluctuations.

Main Results:

• NRXY models exhibit a metastable long-range ordered phase, similar to constant-density flocks.
• The lattice inevitably induces anisotropy, limiting the correlation length.
• Fluctuations generate inescapable anisotropy, even without explicit interaction rules.

Conclusions:

• The ordered phase of lattice NRXY models is equivalent to active clock models.
• Lattice effects fundamentally constrain order in these systems.