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.
33 lines
637 B
Makefile
33 lines
637 B
Makefile
PROJECTNAME=interaction boundary bounding_loop dimer_loops dimer_contour
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LIBS=$(notdir $(wildcard libs/*))
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PDFS=$(addsuffix .pdf, $(PROJECTNAME))
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SOURCES=$(addsuffix .tikz.tex, $(PROJECTNAME))
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all: $(PDFS)
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$(PDFS): $(SOURCES) $(LIBS)
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echo $(LIBS)
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pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
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$(SOURCES):
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python3 dimer_conf.py
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$(LIBS):
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ln -fs libs/$@ ./
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clean-libs:
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rm -f $(LIBS)
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clean-aux:
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rm -f $(addsuffix .aux, $(PROJECTNAME))
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rm -f $(addsuffix .log, $(PROJECTNAME))
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clean-tex:
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rm -f $(PDFS)
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clean-sources:
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rm -f $(SOURCES)
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clean: clean-libs clean-aux clean-tex clean-sources
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