Rotational invariance of quadromer correlations on the hexagonal lattice

Details Rotational invariance of quadromer correlations on the hexagonal lattice Rotational invariance of quadromer correlations on the hexagonal lattice

2005-02-23

arxiv.org/abs/math/0502492v1

Advances in Mathematics, 191 (2005), 46-77

Mathematics

Combinatorics

28 pages

Scientific paper

In 1963 Fisher and Stephenson \cite{FS} conjectured that the monomer-monomer
correlation on the square lattice is rotationally invariant. In this paper we
prove a closely related statement on the hexagonal lattice. Namely, we consider
correlations of two quadromers (four-vertex subgraphs consisting of a monomer
and its three neighbors) and show that they are rotationally invariant.

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