84cec16dd8
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.
41 lines
1.7 KiB
Plaintext
41 lines
1.7 KiB
Plaintext
0.1
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* Changed: Slight change in the statement of the main theorem: no long-range
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positional order between any dimers, regardless of orientation.
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* Changed: Section 4 was completely reworked. It now consists of a
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discussion, in which definitions and figures appear as needed.
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The main lemma of the section was moved to the end.
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* Fixed: The definition of external contours had a serious typo in it.
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* Fixed: The definition of non-trivial polymers was backwards. What were
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called non-trivial polymers are actually trivial, and vice versa.
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* Changed: The contour and polymer figures were changed to include an
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example of a polymer with a non-trivial recursive structure.
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* Fixed: The clusters appearing in cluster expansions must be defined using
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multisets instead of sets, as they were before. The notation was
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adjusted accordingly.
|
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* Fixed: The expression of the Ursell function was missing a combinatorial
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factor.
|
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* Fixed: When splitting a sum over clusters into a sum over a polymer and
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the rest of the cluster, the sum over the multiplictity of the
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polymer must be separated as well, in order to avoid overcounting.
|
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* Fixed: In the proof of lemma 5.2, the bound on \mathfrak x required a
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better estimate on b_+ and nu_+.
|
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* Fixed: In the proof of lemma 5.2, the argument for why the number of bad
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edges on the boundary of \iota is bounded by \ell_0(l-m) was wrong.
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* Added: In the proof of lemma 5.2, a figure was added to illustrate the
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issue with bad edges.
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* Added: Some more minor points have been expanded to include more details.
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* Fixed: Miscellaneous typos and reformating.
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