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Stable spins in the zero temperature spinodal decomposition of 2D Potts models

Author

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  • Derrida, B.
  • de Oliveira, P.M.C.
  • Stauffer, D.

Abstract

We present the results of zero temperature Monte Carlo simulations of the q-state Potts model on a square lattice with either four or eight neighbors, and for the triangular lattice with six neighbors. In agreement with previous works, we observe that the domain growth process gets blocked for the nearest-neighbor square lattice when q is large enough, whereas for the eight neighbor square lattice and for the triangular lattice no blocking is observed. Our simulations indicate that the number of spins which never flipped from the beginning of the simulation up to time t follows a power law as a function of the energy, even in the case of blocking. The exponent of this power law varies from less than sol12 for the Ising case (1q = 2) to 2 for q → ∞ and seems to be universal. The effect of blocking on this exponent is invisible at least up to q = 7.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:phsmap:v:224:y:1996:i:3:p:604-612
    DOI: 10.1016/0378-4371(95)00345-2
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    1. Safran, William, 1983. "France in the Giscard Presidency. By J. R. Frears. (Boston: George Allen & Unwin, 1981. Pp. xii + 224. $24.50, cloth; $10.95, paper.)," American Political Science Review, Cambridge University Press, vol. 77(1), pages 235-236, March.
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    Cited by:

    1. 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.
    2. 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.
    3. Derrida, Bernard, 2021. "Working with Dietrich Stauffer in the ’80s and ’90s," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).

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