Non-reciprocal frustration: time crystalline order-by-disorder phenomenon and a spin-glass-like state

TL;DR

This paper draws an analogy between non-reciprocal active systems and geometrically frustrated systems, revealing how stochastic noise induces symmetry breaking and identifying a spin-glass-like state with unique correlation properties.

Contribution

It establishes a novel analogy between non-reciprocal interactions and frustration, demonstrating noise-induced order-by-disorder phenomena and discovering a spin-glass-like state in such systems.

Findings

Noise induces spontaneous symmetry breaking in non-reciprocal systems.

Identification of a spin-glass-like state with specific correlation decay.

Analogy between non-reciprocal matter and frustrated magnetic systems.

Abstract

Active systems are comprised of constituents with interactions that are generically non-reciprocal in nature. Such non-reciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing its prey, while the prey attempts to evade capture. This situation is somewhat reminiscent of those encountered in geometrically frustrated systems where conflicting objectives also exist, which result in the absence of configurations that simultaneously minimize all interaction energies. In the latter, a rich variety of exotic phenomena are known to arise due to the presence of accidental degeneracy of ground states. In this paper, we establish a direct analogy between these two classes of systems. The analogy is based on the observation that non-reciprocally interacting systems with anti-symmetric coupling and geometrically frustrated systems have in common that they both exhibit marginal orbits, which can be regarded as a dynamical system counterpart of accidentally degenerate ground states. The former is shown by proving a Liouville-type theorem. These ''accidental degeneracies'' of orbits are shown to often get ''lifted'' by stochastic noise or weak random disorder due to the emergent ''entropic force'' to give rise to a noise-induced spontaneous symmetry breaking, in a similar manner to the order-by-disorder phenomena known to occur in geometrically frustrated systems. Furthermore, we report numerical evidence of a non-reciprocity-induced spin-glass-like state that exhibits a short-ranged spatial correlation (with stretched exponential decay) and an algebraic temporal correlation associated with the aging effect. Our work establishes an unexpected connection between the physics of complex magnetic materials and non-reciprocal matter, offering a fresh and valuable perspective for comprehending the latter.