Memory-induced long-range order in dynamical systems

Time non-locality, or memory, is a nonequilibrium property of a physical system characterized by perturbations to the system at one time affecting the system's state at a later time. In this talk, we show that such a property induces spatial long-range order even if the system's units are coupled locally. This happens when the memory degrees of freedom have slower dynamics than the system's degrees of freedom. When the two degrees of freedom have comparable time scales, this long-range order is lost. We exemplify these results with a model of locally coupled spins and a single dynamic memory variable.