Phase Transitions in single species Ising Models with Non-Reciprocal couplings

Abstract

We present a general framework for incorporating non-reciprocal interactions into the Ising model with Glauber dynamics, without requiring multiple species. We then focus on a model with vision-cone type interactions. We solve it in a fully connected network (mean-field) and perform extensive numerical simulations of the model in the square lattice. We find that the breakdown of the spin-flip symmetry introduced by non-reciprocity induces a discontinuous phase transition on top of the usual continuous one, that eventually occurs at higher critical temperatures. Combining a static and dynamic scaling analysis, we measure the critical exponents associated to the continuous symmetry breaking transition, and find them to be identical to the ones of the Ising model in two dimensions (2D), with the exception of the exponent $\beta$ associated to the order parameter. The latter appears to increase as the non-reciprocity of the coupling increases, suggesting that, within our numerical precision, the model does not belong to the 2D Ising model universality class. The coarsening process is anisotropic, but still follows the usual dynamic scaling with an exponent compatible with the standard value with non-conserved order parameter dynamics.