Classical Heisenberg spins with long-range interactions: relaxation to equilibrium for finite systems

Julien Barré 1 Shamik Gupta 2

Journal of Statistical Mechanics: Theory and Experiment, IOP Science, 2014, 2014 (P02017), pp.20. <10.1088/1742-5468/2014/02/P02017>

Systems with long-range interactions often relax towards statistical equilibrium over timescales that diverge with N , the number of particles. A recent work [S. Gupta and D. Mukamel, J. Stat. Mech.: Theory Exp. P03015 (2011)] analyzed a model system comprising N globally coupled classical Heisenberg spins and evolving under classical spin dynamics. It was numerically shown to relax to equilibrium over a time that scales superlinearly with N . Here, we present a detailed study of the Lenard-Balescu operator that accounts at leading order for the finite-N effects driving this relaxation. We demonstrate that corrections at this order are identically zero, so that relaxation occurs over a time longer than of order N , in agreement with the reported numerical results.

  • 1. JAD - Laboratoire Jean Alexandre Dieudonné
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques