Largest lyapunov exponents for lattices of interacting classical spins

A. S. De Wijn, B. Hess, B. V. Fine

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

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.

Original languageEnglish
Article number034101
JournalPhysical Review Letters
Volume109
Issue number3
DOIs
Publication statusPublished - 16 Jul 2012
Externally publishedYes

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