Statistical Mechanics of non−reciprocally interacting Ising spins

Abstract

Non−reciprocal interactions are present in a large number of out−of−equilibrium systems such as active matter, social, ecological and non−Hermitian quantum systems. They are believed to be responsible for non−equilibrium phase transitions and are, still, an open topic of major interest in recent research. In this work, we present a generalization of the Ising model that includes non−reciprocal interactions among spins and analytically characterize the mean field stationary behaviour of two proposed models that incorporate non−reciprocal interactions. We show how the models exhibit a first order phase transition and how their mean field solutions are no longer spin−inversion symmetric. Furthermore, we also study d = 1 spin chains with nearest neighbours interactions, and derive the evolution equations for the first two moments. Finally, we discuss the dynamical equations for the proposed models. The derived dynamic equations signal the presence of steady currents, e.g. traveling states, in non−reciprocally interacting spin chains.