Abstract
Time evolution of a Cellular Automaton that describes shrinking domains is studied. A singly connected domain of Ising spins, embedded in a sea of the opposite phase, develops at T = 0 according to a dynamic rule that does not allow its perimeter to increase. At long enough times the domain disappears; we have shown that the average lifetime of such a domain is proportional to its area. We also considered the T = 0 dynamics of a single infinite quadrant, and have shown that it maps onto a diffusion problem with exclusion in one dimension. This latter problem is mapped onto a critical 6-vertex model.
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References
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© 1989 Springer-Verlag Berlin Heidelberg
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Domany, E., Kandel, D. (1989). Domain Growth Kinetics: Microscopic Derivation of the t½ Law. In: Manneville, P., Boccara, N., Vichniac, G.Y., Bidaux, R. (eds) Cellular Automata and Modeling of Complex Physical Systems. Springer Proceedings in Physics, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75259-9_9
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DOI: https://doi.org/10.1007/978-3-642-75259-9_9
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