Exact enumeration of long-range-ordered dimer coverings on the square-planar lattice.
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It is noted that there occur different classes of complete dimer coverings (Kekul structures) on the square-planar lattice. Each class is characterized by a different degree of long-range ordering in the relative numbers of dimers crossing lines drawn diagonally across the lattice. Asymptotically exact enumerations for these classes as a function of the extent of ordering are obtained via a transfer-matrix technique. 1990 The American Physical Society.