Ising model with non-reciprocal interactions

Effective interactions that violate Newton's third law of action-reaction symmetry are common in systems where interactions are mediated by a non-equilibrium environment. Extensive Monte Carlo simulations are carried out on a two-dimensional Ising model, where the interactions are modified non-reciprocally. We demonstrate that the critical temperature decreases as the non-reciprocity increases and this decrease depends only on the magnitude of non-reciprocity. Further, travelling spin waves due to the local fluctuations in magnetisation are observed and these spin waves travel opposite to the non-reciprocity vector.