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Random-field Ising model for the hysteresis of the prewetting transition on a disordered substrate

Author

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  • Blossey, R.
  • Kinoshita, T.
  • Dupont-Roc, J.

Abstract

We study the effect of substrate randomness on the dynamics of a prewetting transition. The prewetting system is mapped to a 2D-random-field Ising model (RFIM) in an external field H, in which the Ising spins ±1 are identified with a wet or nonwet patch of surface. The model is studied in a cylindrical geometry at zero temperature by simulations with a single-spin-flip rule for the dynamics. The total coverage C and the coverage Cb connected to an initially flipped border are both considered, which correspond to physical quantities actually measured in experiments. Ramping the external field H up and down produces smooth and hysteretic curves for C and Cb. The covering of the substrate appears to be a critical transition for Cb occurring at a nonzero critical field Hc. While the growth exponents are compatible with those of percolation, the thresholds Hc depend in a complex way on the disorder strength. Analytical expressions are proposed for Hc in the weak and strong disorder limits, corresponding to two different growth mechanisms.

Suggested Citation

  • Blossey, R. & Kinoshita, T. & Dupont-Roc, J., 1998. "Random-field Ising model for the hysteresis of the prewetting transition on a disordered substrate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 248(3), pages 247-272.
    • Handle: RePEc:eee:phsmap:v:248:y:1998:i:3:p:247-272
    DOI: 10.1016/S0378-4371(97)00524-4
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    References listed on IDEAS

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    1. Backx, G. & Indekeu, J.O., 1995. "Interface potentials and physical constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 218(1), pages 69-76.
    2. Wehrung, Donald A & Lee, Kam-Hon & Tse, David K. & Vertinsky, Ilan B., 1989. "Adjusting Risky Situations: A Theoretical Framework and Empirical Test," Journal of Risk and Uncertainty, Springer, vol. 2(2), pages 189-212, June.
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