Nonreciprocal Ising model and the Kitaev-Hatano-Nelson chain.

Nonreciprocity is a hallmark of nonequilibrium systems across soft and active matter, open quantum platforms, population dynamics, and neuroscience. We show that the nonreciprocal Ising model, a paradigmatic soft-matter system, is exactly dual to the Kitaev–Hatano–Nelson chain, a central model in open quantum physics. This mapping extends to a broader duality web that also includes a nonreciprocal anisotropic XY model and a nonreciprocal cluster model. We characterize their phase diagrams, identifying exceptional critical lines separated by multicritical points with dynamical exponent $z=2$. Where possible, we provide analytic solutions and clarify when, where, and how members of the duality web should be regarded as quantum versus classical nonequilibrium theories.