Non-reciprocal interactions spatially propagate fluctuations in a 2D Ising model

TL;DR

This paper introduces a 2D Ising model with anisotropic, non-reciprocal interactions inspired by fish behavior, revealing altered critical temperatures and traveling spin waves controllable by interaction parameters.

Contribution

It demonstrates how non-reciprocal interactions modify phase transition properties and induce traveling waves in a 2D Ising model, extending understanding of out-of-equilibrium spin systems.

Findings

Non-reciprocal interactions shift the critical temperature.

Traveling spin waves emerge from local perturbations.

Wave speed and direction are controllable via interaction parameters.

Abstract

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.