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

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.

Expanded version; 24 pages, 16 figures

References in corpus (12)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Nonreciprocal Photon Transmission and Amplification via Reservoir Engineering
• Odd dynamics of living chiral crystals
• Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets
• Nonreciprocity as a generic route to traveling states
• Active phase separation by turning toward regions of higher density
• Long-range Order and Directional Defect Propagation in the Nonreciprocal XY Model with Vision Cone Interactions
• Shear diversity prevents collective synchronization
• The non-reciprocal Dicke model
• Prethermal nematic order and staircase heating in a driven frustrated Ising magnet with dipolar interactions
• Prethermal time-crystalline spin ice and monopole confinement in a driven magnet

Cited by in corpus (24)

• Nonreciprocal Synchronization of Active Quantum Spins
• Non-reciprocal alignment induces asymmetric clustering in active mixtures
• Phase Coexistence in Nonreciprocal Quorum-Sensing Active Matter
• Non-reciprocal breathing solitons
• Phase Transitions in Nonreciprocal Driven-Dissipative Condensates
• Nonreciprocal Spin-Glass Transition and Aging
• Nonreciprocal interactions induce frequency shifts in superradiant lasers
• Dynamical Theory for Adaptive Systems
• Quantum synchronization blockade induced by nonreciprocal coupling
• Kardar-Parisi-Zhang scaling in time-crystalline matter
• Local Order Controls the Onset of Oscillations in the Nonreciprocal Ising Model
• Phase Transitions in single species Ising Models with Non-Reciprocal couplings
• Flocking with random non-reciprocal interactions
• Continuous-time multifarious systems -- Part II: non-reciprocal multifarious self-organization
• Dissipative phase transition of interacting non-reciprocal fermions
• Breaking Mechanical Holography in Combinatorial Metamaterials
• More is less in unpercolated active solids
• Solving the Kinetic Ising Model with Non-Reciprocity
• Far-from-equilibrium complex landscapes
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Dynamics and chaotic properties of the fully disordered Kuramoto model
• Crystallization of Chiral Active Brownian Particles at Low Densities
• Zero-temperature dynamics of the spherical model with non-reciprocal interactions
• Interacting many-body non-Hermitian systems as Markov chains