2001/08/09 by Marie-Christine Firpo, M. -C. Firpo, Stefano Ruffo +1 · 3 citations
Physics and Astronomy · #Quantum chaos and dynamical systems #Scientific Research and Discoveries #Statistical Mechanics and Entropy #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.1088/0305-4470/34/37/102
10 pages, 3 eps figures
arxiv created 2001/08/09 · openalex publication_date 2001/09/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We consider the class of long-range Hamiltonian systems first introduced by Anteneodo and Tsallis and called the α- XY model. This involves N classical rotators on a d -dimensional periodic lattice interacting all to all with an attractive coupling whose strength decays as r -α , r being the distance between sites. Using a recent geometrical approach, we estimate for any d -dimensional lattice the scaling of the largest Lyapunov exponent (LLE) with N as a function of α in the large energy regime where rotators behave almost freely. We find that the LLE vanishes as N -κ , with κ = 1/3 for 0⩽α/ d ⩽1/2 and κ = 2/3(1-α/ d ) for 1/2⩽α/ d <1. These analytical results present a nice agreement with numerical results obtained by Campa et al , including deviations at small N .