Memory-induced long-range order drag

TL;DR

This paper demonstrates that memory-induced long-range order can be propagated through coupled systems without memory, enabling layers without intrinsic memory to sustain long-range order via a drag effect, with implications for neuroscience and neuromorphic systems.

Contribution

It introduces a generic mechanism for transferring memory-induced long-range order across layers lacking memory, supported by analytical and simulation results.

Findings

Memory-induced long-range order can be dragged across layers without memory.

Downstream layers can sustain long-range order despite local interactions and no memory.

The mechanism has implications for brain cortex and neuromorphic system design.

Abstract

Recent research has shown that memory, in the form of slow degrees of freedom, can induce a phase of long-range order (LRO) in locally-coupled fast degrees of freedom, producing power-law distributions of avalanches. In fact, such memory-induced LRO (MILRO) arises in a wide range of physical systems. Here, we show that MILRO can be transferred to coupled systems that have no memory of their own. As an example, we consider a stack of layers of spins with local feedforward couplings: only the first layer contains memory, while downstream layers are memory-free and locally interacting. Analytical arguments and simulations reveal that MILRO can indeed drag across the layers, enabling downstream layers to sustain intra-layer LRO despite having neither memory nor long-range interactions. This establishes a simple, yet generic mechanism for propagating collective activity through media without fine tuning to criticality, with testable implications for neuromorphic systems and laminar information flow in the brain cortex.