Abstract
We study a simple model of the zero-temperature stochastic dynamics for interfaces in two dimensions-essentially Glauber dynamics of the two-dimensional Ising model atT=0. Using elementary geometric considerations, we show that the (rescaled) volume of an initially square droplet decreases linearly to zero as a function of (rescaled) time.
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References
L. Chayes and G. Swindle, Hydrodynamic limits for one-dimensional particle systems with moving boundaries, submitted.
D. A. Huse and D. S. Fisher, Dynamics of droplet fluctuations in pure and random Ising systems,Phys. Rev. B 35:6841–6846 (1987).
M. A. Katsoulakis and P. E. Souganidis, Generalized motion by mean curvature as a macroscopic limit of stochastic Ising models with long range interactions and Glauber dynamics, preprint.
J. Lamperti,Stochastic Processes: A Survey of the Mathematical Theory (Springer-Verlag, Berlin, 1977).
I. M. Lifshitz, Kinetics of ordering during second-order transitions,Phys. JETP 15:939–942 (1962).
T. M. Liggett,Interacting Particle Systems (Springer-Verlag, Berlin, 1985).
H. Rost, Nonequilibrium behavior of a many particle process: Density profile and local equilibrium,Z. Wahrsch. Verw. Gebiete 58:41–43 (1981).
H. Spohn, Interface motion in models with stochastic dynamics,J. Stat. Phys. 71:1081–1131 (1993).
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Chayes, L., Schonmann, R.H. & Swindle, G. Lifshitz' law for the volume of a two-dimensional droplet at zero temperature. J Stat Phys 79, 821–831 (1995). https://doi.org/10.1007/BF02181205
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DOI: https://doi.org/10.1007/BF02181205