1.0 Version bump (no changes) 0.1 * Changed: Slight change in the statement of the main theorem: no long-range positional order between any dimers, regardless of orientation. * Changed: Section 4 was completely reworked. It now consists of a discussion, in which definitions and figures appear as needed. The main lemma of the section was moved to the end. * Fixed: The definition of external contours had a serious typo in it. * Fixed: The definition of non-trivial polymers was backwards. What were called non-trivial polymers are actually trivial, and vice versa. * Changed: The contour and polymer figures were changed to include an example of a polymer with a non-trivial recursive structure. * Fixed: The clusters appearing in cluster expansions must be defined using multisets instead of sets, as they were before. The notation was adjusted accordingly. * Fixed: The expression of the Ursell function was missing a combinatorial factor. * Fixed: When splitting a sum over clusters into a sum over a polymer and the rest of the cluster, the sum over the multiplictity of the polymer must be separated as well, in order to avoid overcounting. * Fixed: In the proof of lemma 5.2, the bound on \mathfrak x required a better estimate on b_+ and nu_+. * Fixed: In the proof of lemma 5.2, the argument for why the number of bad edges on the boundary of \iota is bounded by \ell_0(l-m) was wrong. * Added: In the proof of lemma 5.2, a figure was added to illustrate the issue with bad edges. * Added: Some more minor points have been expanded to include more details. * Fixed: Miscellaneous typos and reformating.