Advanced Computational Methods for Finite-Temperature Magnetization 
Dynamics

Mark A. Novotny, Greg Brown, and Per Arne Rikvold

A number of advanced computational methods for finite-temperature dynamic 
simulations, together with their application to models of magnetic 
materials, will be discussed.  The focus will be both on micromagnetics 
and on dynamic Monte Carlo simualtions.  To bridge the disparate time 
scales, rejection-free dynamic Monte Carlo methods and projective dynamics 
will be discussed [1,2].  To obtain real-time simulations for dynamic 
Monte Carlo requires that the dynamic be obtained from first principles 
from a model Hamiltonian.  Use of the time-dependent quantum density matix 
formalism to obtain such dynamics using a boson heat bath will be 
described [3].  This method is similar to that used to obtain EPR spectra 
of single molecule magnets [4].  An example showing that using the 
incorrect dynamic can give exponentially incorrect results for quantities 
such as the lifetime of a magnetic metastable state will be presented 
[5,6].  Furthermore, the projective dynamics method will be utilized to 
obtain the location of the saddle point for different applied magnetic 
fields in finite-temperature micromagnetic simulations [7,8].  

[1] "A Projection Method for Statics and Dynamics of Lattice Spin 
Systems", M. Kolesik, M.A. Novotny, and P.A. Rikvold, Phys. Rev. Lett., 
vol. 80, 3384-3387 (1998).

[2] "Extreme Long-time Dynamic Monte Carlo Simulations", M. Kolesik, P.A. 
Rikvold, and M.A. Novotny, International Journal of Modern Physics C, 14 
121-132 (2003).  

[3] "Scaling Analysis of a Divergent Prefactor in the Metastable Lifetime 
of a Square-Lattice Ising Ferromagnet at Low Temperatures", K. Park, M.A. 
Novotny, and P.A. Rikvold, Phys. Rev. E, vol. 66, article 056101 [7 pages] 
(2002).

[4] "Role of Dipolar and Exchange Interactions in the Positions and Widths 
of EPR Transitions for the Single-Molecule Magnets Fe_8 and Mn_12", K. 
Park, M.A. Novotny, N.S. Dalal, S. Hill, and P.A. Rikvold, Phys. Rev. B, 
vol. 66, article 144409 [11 pages] (2002). 

[5] "Low-temperature Nucleation in a Kinetic Ising Model with Soft 
Stochastic Dynamics", K. Park, P.A. Rikvold, G.M. Buendia, and M.A. 
Novotny, Phys. Rev. Lett., vol. 92, article 015701 [4 pages] (2004).

[6] "Low-Temperature Nucleation in a Kinetic Ising Model under Different 
Stochastic Dynamics with Local Energy Barriers", G.M. Buendia, P.A. 
Rikvold, K. Park, and M.A. Novotny, J. Chemical Physics, vol. 121, 
4193-4202 (2004).

[7] "Transition State in Magnetization Reversal", G. Brown, M.A. Novotny, 
and P.A. Rikvold, J. Applied Physics, vol. 93, 6817-6819 (2003).  

[8] "Projective Dynamics Analysis of Magnetization Reversal" G. Brown, 
M.A. Novotny, and P.A. Rikvold, Physica B, proceedings for the 4th 
International Symposium on Hysteresis and Micromagnetic Modeling 
(Salamanca, Spain); in press, preprint: cond-mat/0306168.