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

Julien Barré (1) , Shamik Gupta (2)

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

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.

Domaines: Physique [physics]

Julien Barré, Shamik Gupta. Classical Heisenberg spins with long-range interactions: relaxation to equilibrium for finite systems. Journal of Statistical Mechanics: Theory and Experiment, 2014, P02017, pp.20. ⟨10.1088/1742-5468/2014/02/P02017⟩. ⟨hal-01086418⟩