Close-packed dimers on nonorientable surfaces

Wentao T. Lu, F. Y. Wu

Published 2001-10-01, updated 2002-02-18Version 3

The problem of enumerating dimers on an M x N net embedded on non-orientable surfaces is considered. We solve both the Moebius strip and Klein bottle problems for all M and N with the aid of imaginary dimer weights. The use of imaginary weights simplifies the analysis, and as a result we obtain new compact solutions in the form of double products. The compact expressions also permit us to establish a general reciprocity theorem.