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

TL;DR

This paper introduces an exactly solvable one-dimensional non-reciprocal kinetic Ising model, revealing novel non-equilibrium phenomena like underdamped phases, exceptional points, and wave effects driven by non-reciprocity.

Contribution

It provides the first exact solution to a non-reciprocal kinetic Ising model, uncovering new dynamical phases and behaviors induced by non-reciprocal interactions.

Findings

Discovery of underdamped and critically damped phases

Identification of $N^{th}$-order exceptional points

Observation of wave phenomena influenced by system parity

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.