2003/11/16 by Raúl O. Vallejos, Raul O. Vallejos, Celia Anteneodo
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum many-body systems #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2004.04.005
10 pages, 3 figures
arxiv created 2003/11/16 · openalex publication_date 2004/04/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.