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Area of Science:

  • Non-equilibrium statistical mechanics
  • Condensed matter physics
  • Complex systems

Background:

  • Time nonlocality, or memory, is a universal property of physical systems operating out of equilibrium.
  • Typically, spatial long-range order (LRO) arises from long-range interactions.
  • The role of memory in inducing LRO in locally coupled systems remains underexplored.

Purpose of the Study:

  • To investigate if memory, a property of dynamical variables, can induce spatial long-range order (LRO) in systems with only local couplings.
  • To elucidate the mechanism by which memory mediates LRO.
  • To explore the influence of the relative timescales of memory and primary variables on LRO.

Main Methods:

  • Theoretical analysis of systems with memory degrees of freedom.
  • Modeling locally coupled systems with a dynamic memory variable.
  • Investigating the system's behavior through the lens of correlated percolation transitions.

Main Results:

  • Memory is demonstrated to be sufficient for inducing a phase of spatial LRO, even with local primary couplings.
  • The emergence of LRO is contingent on memory degrees of freedom possessing slower dynamics compared to primary variables.
  • The memory-mediated LRO phase is nonperturbative and can be understood as a correlated percolation transition.
  • Comparable timescales between memory and primary variables lead to a reduction in the effective interaction range.

Conclusions:

  • Memory can act as a crucial factor in establishing spatial long-range order in diverse physical systems.
  • The findings suggest a broader applicability of memory-induced LRO beyond the specific models studied.
  • This work highlights a novel mechanism for generating order in non-equilibrium systems through inherent memory effects.