Largest Lyapunov exponent of long-range XY systems

Raúl O Vallejos and Celia Anteneodo

Physica A: Statistical Mechanics and its Applications, 2004, vol. 340, issue 1, 178-186

Abstract: We calculate analytically the largest Lyapunov exponent of the so-called αXY Hamiltonian in the high-energy regime. This system consists of a d-dimensional lattice of classical spins with interactions that decay with distance following a power law, the range being adjustable. In disordered regimes the Lyapunov exponent can be easily estimated by means of the “stochastic approach”, a theoretical scheme based on van Kampen's cumulant expansion. The stochastic approach expresses the Lyapunov exponent as a function of a few statistical properties of the Hessian matrix of the interaction that can be calculated as suitable microcanonical averages. We have verified that there is a very good agreement between theory and numerical simulations.

Keywords: Lyapunov exponents; Long-range interactions (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:340:y:2004:i:1:p:178-186

DOI: 10.1016/j.physa.2004.04.005

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