The probability P ht of a randomly generated free-surface film being in the high temperature partition plotted as a function of the concentration c of up spins. A variety of values of the film thickness W and area L × L are represented. Each curve involves averaging over 500 initial configurations.
The threshold concentration for the free film (filled circles), and the coated film (open triangles), and (filled triangles) are plotted over a range of surface areas L × L. The gap in concentration between the circles and the triangles represent the concentration range for which the arrested film can be formed. Note that .
Plots from two different starting configurations of the evolution of the up spin showing a sequence of concentration profiles with the number of updates (roughly, the “time” step) indicated. An initial concentration of c = 0.09 (∼c cross) was used in each case and W = 500 and L = 500. The free surface is at layer 500 and the profiles are propagating from right to left. (Upper panel) An example of front propagation. (Lower panel) An example of the relaxation occurring at internal relaxation centres.
(a) A projection along the surface normal of the coated film at c = 0.09, W = 100, and L = 800. The image is taken 400 steps into the annealing run. The density of up spins along each column is coded into a gray scale with black indicating zero up spins and white indicating all up. Overlaps correspond to growing domains at different heights. (b) As for (a) except the spin concentration has been increased to c = 0.1. (c) As for (a) except the thickness has been increased to W = 300. Note the higher projected density of growth sites. The grayer shades are a reflection of the increased extent of down flips above and below the growing domains.
The probability P ht of a randomly generated coated-surface film with patch being in the high temperature partition plotted as a function of the size of the patch for up spin concentrations in the range 0.05 ⩽ c ⩽ 0.09. These calculations were carried out on films with W = 400 and L = 400 for which c cross ∼ 0.09. Each curve involves averaging over 500 initial configurations.
A plot of the log of the critical patch size against log(c-c cluster). The value of c cluster = 0.0292 was obtained by fitting. The straight line corresponds to the power law in Eq. (5) .
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