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Survivors in the two-dimensional Potts model: zero-temperature dynamics for Q = ∞

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  • Hennecke, Michael

Abstract

The dynamics of the fraction of never flipped spins F(t) and the average domain area A(t) of the two-dimensional, infinite-Q Potts model are investigated by zero-temperature Monte Carlo simulations. It is shown that the exponents α of algebraic growth of A(t) and Θ of algebraic decay of F(t) are only effective exponents even for very large systems and long times. Their values increase from about 0.9 for short times to almost unity at late times. The fraction of never flipped spins follows a much better power law when viewed as a function of the average domain area, which is the characteristic size in the system. An exponent of Θ′ = 0.98 ± 0.01 is obtained for the decay of F(A) in the whole time interval, consistent with linear behavior.

Suggested Citation

  • Hennecke, Michael, 1997. "Survivors in the two-dimensional Potts model: zero-temperature dynamics for Q = ∞," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 519-528.
    • Handle: RePEc:eee:phsmap:v:246:y:1997:i:3:p:519-528
    DOI: 10.1016/S0378-4371(97)00372-5
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    References listed on IDEAS

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    1. Michael Hennecke, 1997. "Markov Chain Analysis of Single Spin Flip Ising Simulations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 207-227.
    2. Dietrich Stauffer, 1997. "Universality of Derrida Coarsening in Ising Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 361-364.
    3. Derrida, B. & de Oliveira, P.M.C. & Stauffer, D., 1996. "Stable spins in the zero temperature spinodal decomposition of 2D Potts models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 224(3), pages 604-612.
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    Cited by:

    1. Hennecke, Michael, 1998. "Survivors in the two-dimensional Potts model: zero-temperature dynamics for finite Q," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 252(1), pages 173-177.

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