Lyapunov instabilities in lattices of interacting classical spins at infinite temperature

TL;DR

This study numerically explores Lyapunov instabilities in classical spin lattices across different dimensions at infinite temperature, analyzing how spectra depend on lattice size and interaction anisotropy.

Contribution

It provides comprehensive Lyapunov spectra for various lattice types and interaction parameters, highlighting size independence and the effects of anisotropy.

Findings

Lyapunov spectra become size-independent quickly

Largest Lyapunov exponents depend on interaction anisotropy

Differences observed between bipartite and nonbipartite lattices

Abstract

We numerically investigate Lyapunov instabilities for one-, two- and three-dimensional lattices of interacting classical spins at infinite temperature. We obtain the largest Lyapunov exponents for a very large variety of nearest-neighbor spin-spin interactions and complete Lyapunov spectra in a few selected cases. We investigate the dependence of the largest Lyapunov exponents and whole Lyapunov spectra on the lattice size and find that both quickly become size-independent. Finally, we analyze the dependence of the largest Lyapunov exponents on the anisotropy of spin-spin interaction with the particular focus on the difference between bipartite and nonbipartite lattices.