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.

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Journal Physica A
Citation
Paraskevaidis, C.E, Taylor, P.L, Mulder, B.M, & Papatriantafillou, C. (1998). Discrete anchoring: Bulk-substrate coupling in lattice models. Physica A, 250, 517–435.