Characterizing Inference of Non-reciprocal Connections in the Kinetic Ising Model

Non-reciprocal Ising models differ from the traditional Ising model because the coupling of spin i with spin j is not equal to that of j with i. Systems with asymmetric couplings like this are known to exhibit rich phase diagrams and novel nonequilibrium collective behavior. Furthermore, many complex systems in biological settings are known to have individual units whose interactions are not reciprocal, for example the coupling from excitatory to inhibitory neurons will differ in sign to the coupling from inhibitory to excitatory. Here we investigate the discernibility of the existence of a connection between two spins in models with different non-reciprocal interactions. Specifically, we tune the reciprocal coupling strength, non-reciprocal coupling strength, and the temperature of the kinetic Ising model to tune between a quasi-ordered state, disordered state, and the more interesting dynamical swapping state, in which sub-populations magnetize out of phase from each other. We demonstrate values of the thermodynamic variables of the system for optimal discernibility of the existence of underlying couplings, thereby furthering our understanding of the ability to infer non-reciprocal connections in real data and how this can help elucidate nonequilibrium collective behavior.