6533b7d1fe1ef96bd125c21e
RESEARCH PRODUCT
ORDERING KINETICS IN QUASI-ONE-DIMENSIONAL ISING-LIKE SYSTEMS
Marcus MüllerWolfgang Paulsubject
Stochastic processLattice (order)Logarithmic growthMonte Carlo methodStatistical and Nonlinear PhysicsIsing modelStatistical physicsStatistical mechanicsStructure factorRandom walkMathematical PhysicsMathematicsdescription
We present results of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in anL xM geometry with two free boundaries of length M≫L. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthL. We follow the ordering kinetics after quenches to temperatures 0.25 ⩽ T/Tc ⩽ 1 starting from a random initial configuration at a coverage ofΘ=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short initial two-dimensional ordering process through a crossover region to a quasi-one-dimensional behavior. The whole process is diffusive (inverse half-width of the structure factor peak 1/Δq¦¦ ∝ √t), in contrast to a model proposed by Kawasakiet al., where an intermediate logarithmic growth law is expected. All results are completely describable in the picture of an annihilating random walk (ARW) of domain walls.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1993-10-01 |