From 84cec16dd8bbab11a43f00380a1e6354e3aa0c04 Mon Sep 17 00:00:00 2001 From: Ian Jauslin Date: Wed, 25 Apr 2018 22:10:43 +0000 Subject: Update to v0.1: 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. --- Changelog | 40 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 40 insertions(+) create mode 100644 Changelog (limited to 'Changelog') diff --git a/Changelog b/Changelog new file mode 100644 index 0000000..7bb84a0 --- /dev/null +++ b/Changelog @@ -0,0 +1,40 @@ +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. -- cgit v1.2.3-70-g09d2