BIT Numerical Mathematics

, Volume 44, Issue 3, pp 403–424

An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models


DOI: 10.1023/B:BITN.0000046812.08252.34

Cite this article as:
Arponen, T. & Leimkuhler, B. BIT Numerical Mathematics (2004) 44: 403. doi:10.1023/B:BITN.0000046812.08252.34


(Anti)-/ferromagnetic Heisenberg spin models arise from discretization of Landau–Lifshitz models in micromagnetic modelling. In many applications it is essential to study the behavior of the system at a fixed temperature. A formulation for thermostatted spin dynamics was given by Bulgac and Kusnetsov, which incorporates a complicated nonlinear dissipation/driving term while preserving spin length. It is essential to properly model this term in simulation, and simplified schemes give poor numerical performance, e.g., requiring an excessively small timestep for stable integration. In this paper we present an efficient, structure-preserving method for thermostatted spin dynamics.

Heisenberg ferromagnet micromagnetics spin dynamics Landau–Lifschitz equation Gilbert damping thermostats constant temperature domain walls geometric integrator reversible method 

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Institute of MathematicsHelsinki University of TechnologyHUTFinland. email
  2. 2.Department of MathematicsUniversity of LeicesterLeicesterU.K.

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