Largest Lyapunov exponent of long-range XY systems

Details Largest Lyapunov exponent of long-range XY systems Largest Lyapunov exponent of long-range XY systems

2003-11-16

arxiv.org/abs/cond-mat/0311367v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, 3 figures

Scientific paper

10.1016/j.physa.2004.04.005

We calculate analytically the largest Lyapunov exponent of the so-called $\alpha XY$ 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.

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