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Discrete anchoring: Bulk-substrate coupling in lattice models

Author

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  • Paraskevaidis, C.E
  • Taylor, P.L
  • Mulder, B.M
  • Papatriantafillou, C

Abstract

We formulate the anchoring problem for discrete-state lattice models. Anchoring is the selection of a bulk equilibrium state from a degenerate set of equivalent equilibrium states in semi-infinite samples in contact with a substrate, a phenomenon widely discussed in the context of liquid crystalline displays. As a concrete example we consider this problem for the three-state Potts model employing two different approximations, viz., a layered mean-field approximation and a Bethe lattice approach. The anchoring behaviour of the model is shown to be completely determined by the symmetry properties of the Hamiltonian.

Suggested Citation

  • Paraskevaidis, C.E & Taylor, P.L & Mulder, B.M & Papatriantafillou, C, 1998. "Discrete anchoring: Bulk-substrate coupling in lattice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 517-534.
    • Handle: RePEc:eee:phsmap:v:250:y:1998:i:1:p:517-534
    DOI: 10.1016/S0378-4371(97)00566-9
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