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Nonreciprocal systems exhibit complex dynamics. This study reveals that static order is fragile in lower dimensions, while a time-dependent "swap phase" is stabilized in 3D, altering critical behavior and creating a spatial clock.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Condensed Matter Physics

Background:

  • Systems with nonreciprocal interactions often show time-dependent states and oscillations.
  • The stability and phase transitions of these states in noisy, extended systems are not fully understood.

Purpose of the Study:

  • Investigate the stability of nonreciprocal phases in spatially-extended systems.
  • Analyze the critical behavior of phase transitions in a nonreciprocal Ising model.
  • Understand the role of dimensionality and noise in these systems.

Main Methods:

  • Introduced a nonreciprocal generalization of the Ising model.
  • Employed analytical and large-scale numerical simulations.
  • Examined phase transitions and critical phenomena.

Main Results:

  • Mean-field predictions of three stable phases differ from simulation results.
  • Static order is destroyed by droplet growth in finite dimensions unless symmetry is broken.
  • The time-dependent swap phase is unstable in 2D but stabilized in 3D.
  • Nonreciprocity alters critical exponents from Ising to XY in 3D, forming a spatial clock.

Conclusions:

  • Static order in nonreciprocal systems is sensitive to dimensionality and noise.
  • The thermodynamic limit reveals distinct behaviors compared to finite systems.
  • 3D nonreciprocal systems exhibit unique critical phenomena and emergent spatial order.