Journal of Statistical Physics

, Volume 119, Issue 1–2, pp 347–389 | Cite as

Mesoscopic Modeling for Continuous Spin Lattice Systems: Model Problems and Micromagnetics Applications

  • Markos A. Katsoulakis
  • Petr Plecháč
  • Dimitrios K. Tsagkarogiannis


In this paper we derive deterministic mesoscopic theories for model continuous spin lattice systems both at equilibrium and non-equilibrium in the presence of thermal fluctuations. The full magnetic Hamiltonian that includes singular integral (dipolar) interactions is also considered at equilibrium. The non-equilibrium microscopic models we consider are relaxation-type dynamics arising in kinetic Monte Carlo or Langevin-type simulations of lattice systems. In this context we also employ the derived mesoscopic models to study the relaxation of such algorithms to equilibrium


Heisenberg spin lattice system Kac potential large deviations statistical equilibrium Monte Carlo methods relaxation dynamics 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Markos A. Katsoulakis
    • 1
  • Petr Plecháč
    • 2
  • Dimitrios K. Tsagkarogiannis
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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