Motivated by the anisotropic interactions between fish, we implement spatially anisotropic and therefore non-reciprocal interactions in the 2D Ising model. First, we show that the model with non-reciprocal interactions alters the system critical temperature away from that of the traditional 2D Ising model. Further, local perturbations to the magnetization in this out-of-equilibrium system manifest themselves as traveling waves of spin states along the lattice, also seen in a mean-field model of our system. The speed and directionality of these traveling waves are controllable by the orientation and magnitude of the non-reciprocal interaction kernel as well as the proximity of the system to the critical temperature.
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Nonreciprocal Pattern Formation of Conserved Fields
In recent years, non-reciprocally coupled systems have received growing attention. Previous work has shown that the interplay of non-reciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We show that these phenomena are generically found in a broad class of pattern-forming systems, including mass-conserving reaction--diffusion systems and viscoelastic active gels. All these systems share a characteristic dispersion relation that acquires a non-zero imaginary part at the edge of the band of unstable modes and exhibit a regime of propagating structures (traveling wave bands or droplets). We show that models for these systems can be mapped to a common ``normal form'' that can be seen as a spatially extended generalization of the FitzHugh--Nagumo model, providing a unifying dynamical-systems perspective. We show that the minimal non-reciprocal Cahn--Hilliard (NRCH) equations exhibit a surprisingly rich set of behaviors, including interrupted coarsening of traveling waves without selection of a preferred wavelength and transversal undulations of wave fronts in two dimensions. We show that the emergence of traveling waves and their speed are precisely predicted from the local dispersion relation at interfaces far away from the homogeneous steady state. The traveling waves are therefore a consequence of spatially localized coalescence of hydrodynamic modes arising from mass conservation and translational invariance of displacement fields. Our work thus generalizes previously studied non-reciprocal phase transitions and identifies generic mechanisms for the emergence of dynamical patterns of conserved fields.
more » « less- Award ID(s):
- 2041459
- PAR ID:
- 10535384
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review X
- Volume:
- 14
- Issue:
- 2
- ISSN:
- 2160-3308
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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