Largest Lyapunov exponents for lattices of interacting classical spins

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.

Cited by in corpus (4)

• 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
• Free induction decays in nuclear spin-1/2 lattices with small number of interacting neighbors: the cases of silicon and fluorapatite
• Persistent many-body quantum echoes