ScienceAsia 29 (2003): 279-289 |doi: 10.2306/scienceasia1513-1874.2003.29.279

Random Walk on a Plane-Spin-Rotator System: Continuum Theory and Monte Carlo Simulations

Wannapong Triampo^a,d,*, Darapond Triampo^b, I-Ming Tang^a,d and Yongwimon Lenbury^c

ABSTRACT: We introduce a Plane-Spin-Rotator (PSR) model as one of a myriad of non-equilibrium statistical mechanics models governed by stochastic dynamics. The system consists of a one-dimensional chain of lattice sites in which each site is attached with a spin initially in the ordered state e.g., pointing in the same direction. We incorporate the effects of a non-equilibrium phenomenon by giving the system a dynamics. Namely we put a random walker (RW) or a Brownian agent at the origin or in the middle of the lattice chain at the beginning and let it execute pure unbiased random walk to disorder i.e., to destroy the line up of the spins. The local update rule whereby the system changes periodically from one state to another is that each time step as the RW moves it has a certain probability to rotate the spin or change the angle (x ,t) between the x-axis and the spin. We find the nontrivial statistics (x ,t) of due to this and other simple stochastic (Markovian type) model such as [cos (0,t)] and [sin (0,t)] do not behave in sinusoidal fashion as one might expect. These functions and other can be calculated analytically exploiting the results from its “cousin” model introduced in Physical Review E, Volume 59, no. 5 p.5127. Excellent agreement from theoretical and Monte Carlo computer simulation results is found.

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a Department of Physics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand.
b Department of Chemistry, Faculty of Science, Mahidol University, Bangkok 10400, Thailand.
c Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand.
d Capability Building Unit in Nanoscience and Nanotechnology, Faculty of Science, Mahidol University, Bangkok 10400, Thailand.

* Corresponding author, Email: wtriampo@yahoo.com

Received 2 Jan 2003, Accepted 21 Feb 2003