An Exact Solution for the Kinetic Ising Model with Non-Reciprocity

Abstract: A wide range of non-equilibrium phenomena in nature involve non-reciprocal interactions. To understand the novel behaviors that can emerge in such systems, finding tractable models is essential. With this goal, we introduce a non-reciprocal generalization of the kinetic Ising model in one dimension and solve it exactly. Our solution uncovers novel properties driven by non-reciprocity, such as underdamped phases, critically damped phases where a system of size $N$ is described by an $N^{th}$-order exceptional point, and wave phenomena influenced by the parity of $N$. Additionally, we examine the low-energy behavior of these systems in various limits, demonstrating that non-reciprocity leads to unique scaling behavior at zero temperature.