  Time non-locality, or memory, is a non-equilibrium property shared by all
physical systems. It means that when a system's state is perturbed, it is still
affected by the perturbation at a later time. Here, we show that such a memory
effect is sufficient to induce a phase of spatial long-range order (LRO) even
if the system's dynamical variables are coupled locally. This occurs when the
memory degrees of freedom have slower dynamics than the system's degrees of
freedom. In addition, such a LRO phase is non-perturbative and attractive to
the system, but its existence does not necessarily imply criticality. When the
two degrees of freedom have comparable time scales, the length of the effective
long-range interaction shortens. We exemplify this behavior with a model of
locally coupled spins and a single dynamic memory variable, but our analysis is
sufficiently general to suggest that memory could induce a phase of LRO in a
much wider variety of physical systems.
