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Title: Mapping the Monte Carlo scheme to langevin dynamics: A fokker-planck approach
Authors: Cheng, X.Z. 
Jalil, M.B.A. 
Lee, H.K.
Okabe, Y.
Issue Date: 2006
Source: Cheng, X.Z., Jalil, M.B.A., Lee, H.K., Okabe, Y. (2006). Mapping the Monte Carlo scheme to langevin dynamics: A fokker-planck approach. Physical Review Letters 96 (6) : -. ScholarBank@NUS Repository.
Abstract: We propose a general method of using the Fokker-Planck equation (FPE) to link the Monte Carlo (MC) and the Langevin micromagnetic schemes. We derive the drift and diffusion FPE terms corresponding to the MC method and show that it is analytically equivalent to the stochastic Landau-Lifshitz-Gilbert (LLG) equation of Langevin-based micromagnetics. Subsequent results such as the time-quantification factor for the Metropolis MC method can be rigorously derived from this mapping equivalence. The validity of the mapping is shown by the close numerical convergence between the MC method and the LLG equation for the case of a single magnetic particle as well as interacting arrays of particles. We also find that our Metropolis MC method is accurate for a large range of damping factors α, unlike previous time-quantified MC methods which break down at low α, where precessional motion dominates. © 2006 The American Physical Society.
Source Title: Physical Review Letters
ISSN: 00319007
DOI: 10.1103/PhysRevLett.96.067208
Appears in Collections:Staff Publications

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