An Exact Solution to the Kinetic Ising Model with Non-Reciprocity in 1D

Many non-equilibrium physical systems involve the presence of non-reciprocal interactions. These non-reciprocal interactions allow for the development of new phenomena that are difficult to study without solvable models. Here we present a generalization of the one-dimensional kinetic Ising model incorporating non-reciprocal interactions and solve it exactly with general coupling parameters. We then examine novel properties present in this non-reciprocal system, such as an underdamped phase, a critically damped phase described by an exceptional point, and unique propagation of excitations. We further show how different boundary conditions modify the dynamics of wave propagation and generalize this method to systems coupled more generally.