Largest Lyapunov exponents for lattices of interacting classical spins
arXiv:1205.2901 · doi:10.1103/PhysRevLett.109.034101
Abstract
We investigate how generic the onset of chaos in interacting many-body classical systems is in the context of lattices of classical spins with nearest neighbor anisotropic couplings. Seven large lattices in different spatial dimensions were considered. For each lattice, more than 2000 largest Lyapunov exponents for randomly sampled Hamiltonians were numerically computed. Our results strongly suggest the absence of integrable nearest-neighbor Hamiltonians for the infinite lattices except for the trivial Ising case. In the vicinity of the Ising case, the largest Lyapunov exponents exhibit a power-law growth, while further away they become rather weakly sensitive to the Hamiltonian anisotropy. We also provide an analytical derivation of these results.
References in corpus (14)
- Lyapunov instability and finite size effects in a system with long-range forces
- Largest Lyapunov Exponent for Many Particle Systems at Low Densities
- The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium
- Goldstone modes in Lyapunov spectra of hard sphere systems
- Universal Long-time Behavior of Nuclear Spin Decays in a Solid
- On the long-time behavior of spin echo and its relation to free induction decay
- Long-time Behavior of Nuclear Spin Decays in Various Lattices
- Eigenmodes in the long-time behavior of a coupled spin system measured with nuclear magnetic resonance
- Long-Time Relaxation on Spin Lattice as Manifestation of Chaotic Dynamics
- Universal Long-Time Relaxation on the Lattices of Classical Spins: Markovian Behavior on non-Markovian Timescales
- Classes of integrable spin systems
- Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems
- Phase relationship between the long-time beats of free induction decays and spin echoes in solids
- Radius of curvature approach to the Kolmogorov-Sinai entropy of dilute hard particles in equilibrium
Cited by in corpus (26)
- Light-cone spreading of perturbations and the butterfly effect in a classical spin chain
- Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
- Temperature dependence of butterfly effect in a classical many-body system
- Classical many-body chaos with and without quasiparticles
- Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
- Sensitivity to small perturbations in systems of large quantum spins
- Signatures of Chaos in Time Series Generated by Many-Spin Systems at High Temperatures
- Lyapunov instabilities in lattices of interacting classical spins at infinite temperature
- Effectiveness of classical spin simulations for describing NMR relaxation of quantum spins
- Extracting Lyapunov exponents from the echo dynamics of Bose-Einstein condensates on a lattice
- Hybrid quantum-classical method for simulating high-temperature dynamics of nuclear spins in solids
- Chaotic properties of spin lattices near second-order phase transitions
- Free induction decays in nuclear spin-1/2 lattices with small number of interacting neighbors: the cases of silicon and fluorapatite
- Genuine quantum scars in many-body spin systems
- Estimating ergodization time of a chaotic many-particle system from a time reversal of equilibrium noise
- Quantum-classical correspondence of strongly chaotic many-body spin models
- Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
- Almost complete revivals in quantum many-body systems
- Chaos enhancement in large-spin chains
- Classical Dynamics of Harmonically Trapped Interacting Particles
- Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
- Persistent many-body quantum echoes
- Classical periodic trajectories and quantum scars in many-spin systems
- Lindblad quantum dynamics from correlation functions of classical spin chains
- Classical spin simulations with a quantum two-spin correction
- Attraction Induced by Mutual Quantum Measurements of Velocity