  We present a Monte Carlo algorithm that provides efficient and unbiased
sampling of polymer melts consisting of two chains of equal length that jointly
visit all the sites of a cubic lattice with rod geometry L x L x rL and
non-periodic (hard wall) boundary conditions. Using this algorithm for chains
of length up to 40 000 monomers and aspect ratios 1 <= r <= 10, we show that in
the limit of a large lattice the two chains phase separate. This demixing
phenomenon is present already for r=1, and becomes more pronounced, albeit not
perfect, as r is increased.
