From 1399f7eea0d4cc4ad16a9ac1b97dda445cbdfba0 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Thu, 9 Mar 2017 18:53:52 -0500 Subject: march meeting pres changes --- aps_mm_2017.aux | 52 ++++---- aps_mm_2017.log | 321 ++++++++++++++++++++++++++++++++++--------------- aps_mm_2017.nav | 52 ++++---- aps_mm_2017.pdf | Bin 232269 -> 401702 bytes aps_mm_2017.synctex.gz | Bin 19629 -> 27461 bytes aps_mm_2017.tex | 125 ++++++++++++++++--- figs/fig7.pdf | Bin 0 -> 21562 bytes figs/fig8.pdf | Bin 0 -> 14915 bytes figs/fig9.pdf | Bin 0 -> 16742 bytes 9 files changed, 396 insertions(+), 154 deletions(-) create mode 100644 figs/fig7.pdf create mode 100644 figs/fig8.pdf create mode 100644 figs/fig9.pdf diff --git a/aps_mm_2017.aux b/aps_mm_2017.aux index 79e4753..8c4ea74 100644 --- a/aps_mm_2017.aux +++ b/aps_mm_2017.aux @@ -20,26 +20,34 @@ \@writefile{nav}{\beamer@endinputifotherversion {3.36pt}} \@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}} \@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{2}{2/5}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {2}{5}}} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{3}{6/8}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {6}{8}}} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{4}{9/11}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {9}{11}}} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{5}{12/13}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {12}{13}}} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{6}{14/15}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {14}{15}}} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{7}{16/17}{}{0}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{2}{2/4}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {2}{4}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{3}{5/8}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {5}{8}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{4}{9/12}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {9}{12}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{5}{13/15}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {13}{15}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{6}{16/17}{}{0}}} \@writefile{nav}{\headcommand {\beamer@framepages {16}{17}}} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{8}{18/18}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {18}{18}}} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{9}{19/19}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {19}{19}}} -\@writefile{nav}{\headcommand {\slideentry {0}{0}{10}{20/20}{}{0}}} -\@writefile{nav}{\headcommand {\beamer@framepages {20}{20}}} -\@writefile{nav}{\headcommand {\beamer@partpages {1}{20}}} -\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{20}}} -\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{20}}} -\@writefile{nav}{\headcommand {\beamer@documentpages {20}}} -\@writefile{nav}{\headcommand {\def \inserttotalframenumber {10}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{7}{18/19}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {18}{19}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{8}{20/21}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {20}{21}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{9}{22/24}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {22}{24}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{10}{25/27}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {25}{27}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{11}{28/29}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {28}{29}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{12}{30/31}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {30}{31}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{13}{32/34}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {32}{34}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{14}{35/35}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {35}{35}}} +\@writefile{nav}{\headcommand {\beamer@partpages {1}{35}}} +\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{35}}} +\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{35}}} +\@writefile{nav}{\headcommand {\beamer@documentpages {35}}} +\@writefile{nav}{\headcommand {\def \inserttotalframenumber {14}}} diff --git a/aps_mm_2017.log b/aps_mm_2017.log index 28f1165..2d088d9 100644 --- a/aps_mm_2017.log +++ b/aps_mm_2017.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016/Arch Linux) (preloaded format=pdflatex 2016.11.28) 1 MAR 2017 08:13 +This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016/Arch Linux) (preloaded format=pdflatex 2016.11.22) 1 MAR 2017 12:23 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -1280,122 +1280,251 @@ LaTeX Font Warning: Font shape `T1/ccr/m/n' in size <4> not available [1 {/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] - + +File: figs/fig7.pdf Graphic file (type pdf) + +Package pdftex.def Info: figs/fig7.pdf used on input line 67. +(pdftex.def) Requested size: 122.91406pt x 85.48048pt. + + +LaTeX Warning: File `susceptibility.jpg' not found on input line 67. + + +./aps_mm_2017.tex:67: Package pdftex.def Error: File `susceptibility.jpg' not f +ound. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.67 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + +LaTeX Font Info: Try loading font information for T1+cmtt on input line 67. +(/usr/share/texmf-dist/tex/latex/base/t1cmtt.fd +File: t1cmtt.fd 2014/09/29 v2.5h Standard LaTeX font definitions +) [2 + + <./figs/fig7.pdf>] +File: figs/fig7.pdf Graphic file (type pdf) + + +Package pdftex.def Info: figs/fig7.pdf used on input line 67. +(pdftex.def) Requested size: 122.91406pt x 85.48048pt. + + +LaTeX Warning: File `susceptibility.jpg' not found on input line 67. + + +./aps_mm_2017.tex:67: Package pdftex.def Error: File `susceptibility.jpg' not f +ound. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.67 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + +[3 + +] +File: figs/fig7.pdf Graphic file (type pdf) + +Package pdftex.def Info: figs/fig7.pdf used on input line 67. +(pdftex.def) Requested size: 122.91406pt x 85.48048pt. + + +LaTeX Warning: File `susceptibility.jpg' not found on input line 67. + + +./aps_mm_2017.tex:67: Package pdftex.def Error: File `susceptibility.jpg' not f +ound. + +See the pdftex.def package documentation for explanation. +Type H for immediate help. + ... + +l.67 \end{frame} + +Using draft setting for this image. +Try typing to proceed. +If that doesn't work, type X to quit. + +[4 + +] File: figs/fig2.png Graphic file (type png) -Package pdftex.def Info: figs/fig2.png used on input line 69. +Package pdftex.def Info: figs/fig2.png used on input line 101. (pdftex.def) Requested size: 122.91406pt x 96.90472pt. - [2 + +[5 <./figs/fig2.png>] File: figs/fig2.png Graphic file (type png) -Package pdftex.def Info: figs/fig2.png used on input line 69. +Package pdftex.def Info: figs/fig2.png used on input line 101. (pdftex.def) Requested size: 122.91406pt x 96.90472pt. - [3 + [6 ] File: figs/fig2.png Graphic file (type png) -Package pdftex.def Info: figs/fig2.png used on input line 69. +Package pdftex.def Info: figs/fig2.png used on input line 101. (pdftex.def) Requested size: 122.91406pt x 96.90472pt. - [4 + [7 ] File: figs/fig2.png Graphic file (type png) - -Package pdftex.def Info: figs/fig2.png used on input line 69. -(pdftex.def) Requested size: 122.91406pt x 96.90472pt. -[5 + +Package pdftex.def Info: figs/fig2.png used on input line 101. +(pdftex.def) Requested size: 122.91406pt x 96.90472pt. + [8 -] +] File: figs/fig3.pdf Graphic file (type pdf) - -Package pdftex.def Info: figs/fig3.pdf used on input line 102. + + +Package pdftex.def Info: figs/fig3.pdf used on input line 136. (pdftex.def) Requested size: 92.1879pt x 94.28166pt. + +File: figs/fig8.pdf Graphic file (type pdf) + + +Package pdftex.def Info: figs/fig8.pdf used on input line 136. +(pdftex.def) Requested size: 92.1879pt x 59.92123pt. + [9 - + <./figs/fig3.pdf> <./figs/fig8.pdf + +pdfTeX warning: pdflatex (file ./figs/fig8.pdf): PDF inclusion: multiple pdfs w +ith page group included in a single page +>] File: figs/fig4.pdf Graphic file (type pdf) -Package pdftex.def Info: figs/fig4.pdf used on input line 102. +Package pdftex.def Info: figs/fig4.pdf used on input line 136. (pdftex.def) Requested size: 92.1879pt x 94.28166pt. - [6 +File: figs/fig8.pdf Graphic file (type pdf) - <./figs/fig3.pdf> <./figs/fig4.pdf + +Package pdftex.def Info: figs/fig8.pdf used on input line 136. +(pdftex.def) Requested size: 92.1879pt x 59.92123pt. + [10 -pdfTeX warning: pdflatex (file ./figs/fig4.pdf): PDF inclusion: multiple pdfs w -ith page group included in a single page ->] -File: figs/fig3.pdf Graphic file (type pdf) - -Package pdftex.def Info: figs/fig3.pdf used on input line 102. -(pdftex.def) Requested size: 92.1879pt x 94.28166pt. + <./figs/fig4.pdf>] File: figs/fig4.pdf Graphic file (type pdf) -Package pdftex.def Info: figs/fig4.pdf used on input line 102. +Package pdftex.def Info: figs/fig4.pdf used on input line 136. (pdftex.def) Requested size: 92.1879pt x 94.28166pt. - [7 +File: figs/fig8.pdf Graphic file (type pdf) + + +Package pdftex.def Info: figs/fig8.pdf used on input line 136. +(pdftex.def) Requested size: 92.1879pt x 59.92123pt. + [11 ] -File: figs/fig3.pdf Graphic file (type pdf) - -Package pdftex.def Info: figs/fig3.pdf used on input line 102. -(pdftex.def) Requested size: 92.1879pt x 94.28166pt. File: figs/fig4.pdf Graphic file (type pdf) - - -Package pdftex.def Info: figs/fig4.pdf used on input line 102. + +Package pdftex.def Info: figs/fig4.pdf used on input line 136. (pdftex.def) Requested size: 92.1879pt x 94.28166pt. - [8 +File: figs/fig8.pdf Graphic file (type pdf) + +Package pdftex.def Info: figs/fig8.pdf used on input line 136. +(pdftex.def) Requested size: 92.1879pt x 59.92123pt. + [12 -] [9 +] [13 -] [10 +] +[14 -] [11 +] [15 -] [12 +] [16 -] [13 +] [17 -] - +] File: figs/fig1.pdf Graphic file (type pdf) - -Package pdftex.def Info: figs/fig1.pdf used on input line 162. + + +Package pdftex.def Info: figs/fig1.pdf used on input line 196. (pdftex.def) Requested size: 215.10196pt x 142.8041pt. - [14 + [18 <./figs/fig1.pdf>] File: figs/fig1.pdf Graphic file (type pdf) -Package pdftex.def Info: figs/fig1.pdf used on input line 162. +Package pdftex.def Info: figs/fig1.pdf used on input line 196. (pdftex.def) Requested size: 215.10196pt x 142.8041pt. - [15 + [19 -] [16 +] [20 -] [17 +] +[21 -] [18 +] [22 -] -Overfull \hbox (9.441pt too wide) detected at line 221 - $[] []$ - [] +] [23 -[19 +] [24 -] +] [25 + +] [26 + +] [27 + +] + +File: figs/fig9.pdf Graphic file (type pdf) + +Package pdftex.def Info: figs/fig9.pdf used on input line 282. +(pdftex.def) Requested size: 184.3758pt x 120.35542pt. + [28 + + <./figs/fig9.pdf>] +File: figs/fig9.pdf Graphic file (type pdf) + +Package pdftex.def Info: figs/fig9.pdf used on input line 282. +(pdftex.def) Requested size: 184.3758pt x 120.35542pt. + [29 + +] + +File: figs/fig6.pdf Graphic file (type pdf) + +Package pdftex.def Info: figs/fig6.pdf used on input line 296. +(pdftex.def) Requested size: 307.28987pt x 159.65544pt. + [30 + + <./figs/fig6.pdf>] File: figs/fig5.pdf Graphic file (type pdf) - -Package pdftex.def Info: figs/fig5.pdf used on input line 227. -(pdftex.def) Requested size: 245.83282pt x 129.92177pt. -[20 + +Package pdftex.def Info: figs/fig5.pdf used on input line 296. +(pdftex.def) Requested size: 307.28987pt x 154.11826pt. + [31 + + <./figs/fig5.pdf>] [32 + +] [33 - <./figs/fig5.pdf>] +] [34 + +] [35 + +] \tf@nav=\write6 \openout6 = `aps_mm_2017.nav'. @@ -1405,11 +1534,12 @@ Package pdftex.def Info: figs/fig5.pdf used on input line 227. \tf@snm=\write8 \openout8 = `aps_mm_2017.snm'. -Package atveryend Info: Empty hook `BeforeClearDocument' on input line 229. -Package atveryend Info: Empty hook `AfterLastShipout' on input line 229. - (./aps_mm_2017.aux) -Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 229. -Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 229. +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 322. +Package atveryend Info: Empty hook `AfterLastShipout' on input line 322. + +(./aps_mm_2017.aux) +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 322. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 322. Package rerunfilecheck Info: File `aps_mm_2017.out' has not changed. (rerunfilecheck) Checksum: D41D8CD98F00B204E9800998ECF8427E;0. @@ -1417,35 +1547,38 @@ Package rerunfilecheck Info: File `aps_mm_2017.out' has not changed. LaTeX Font Warning: Size substitutions with differences (Font) up to 1.0pt have occurred. -Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 229. +Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 322. ) Here is how much of TeX's memory you used: - 17244 strings out of 493013 - 321845 string characters out of 6139316 - 392797 words of memory out of 5000000 - 20291 multiletter control sequences out of 15000+600000 - 18323 words of font info for 52 fonts, out of 8000000 for 9000 + 17356 strings out of 493013 + 324022 string characters out of 6139316 + 394798 words of memory out of 5000000 + 20361 multiletter control sequences out of 15000+600000 + 20567 words of font info for 56 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 - 56i,12n,55p,391b,475s stack positions out of 5000i,500n,10000p,200000b,80000s - {/usr/share/texmf-dist/fonts/enc/dvips/cm-super/cm-s -uper-t1.enc} -Output written on aps_mm_2017.pdf (20 pages, 232269 bytes). + 56i,14n,55p,391b,570s stack positions out of 5000i,500n,10000p,200000b,80000s +{/usr/share/texmf-dist/fonts/enc/dvips/cm-super/cm-super-t1.enc} + +Output written on aps_mm_2017.pdf (35 pages, 401702 bytes). PDF statistics: - 327 PDF objects out of 1000 (max. 8388607) - 214 compressed objects within 3 object streams - 41 named destinations out of 1000 (max. 500000) - 68 words of extra memory for PDF output out of 10000 (max. 10000000) + 544 PDF objects out of 1000 (max. 8388607) + 367 compressed objects within 4 object streams + 71 named destinations out of 1000 (max. 500000) + 88 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/aps_mm_2017.nav b/aps_mm_2017.nav index 2a27aad..f6238fe 100644 --- a/aps_mm_2017.nav +++ b/aps_mm_2017.nav @@ -1,26 +1,34 @@ \beamer@endinputifotherversion {3.36pt} \headcommand {\slideentry {0}{0}{1}{1/1}{}{0}} \headcommand {\beamer@framepages {1}{1}} -\headcommand {\slideentry {0}{0}{2}{2/5}{}{0}} -\headcommand {\beamer@framepages {2}{5}} -\headcommand {\slideentry {0}{0}{3}{6/8}{}{0}} -\headcommand {\beamer@framepages {6}{8}} -\headcommand {\slideentry {0}{0}{4}{9/11}{}{0}} -\headcommand {\beamer@framepages {9}{11}} -\headcommand {\slideentry {0}{0}{5}{12/13}{}{0}} -\headcommand {\beamer@framepages {12}{13}} -\headcommand {\slideentry {0}{0}{6}{14/15}{}{0}} -\headcommand {\beamer@framepages {14}{15}} -\headcommand {\slideentry {0}{0}{7}{16/17}{}{0}} +\headcommand {\slideentry {0}{0}{2}{2/4}{}{0}} +\headcommand {\beamer@framepages {2}{4}} +\headcommand {\slideentry {0}{0}{3}{5/8}{}{0}} +\headcommand {\beamer@framepages {5}{8}} +\headcommand {\slideentry {0}{0}{4}{9/12}{}{0}} +\headcommand {\beamer@framepages {9}{12}} +\headcommand {\slideentry {0}{0}{5}{13/15}{}{0}} +\headcommand {\beamer@framepages {13}{15}} +\headcommand {\slideentry {0}{0}{6}{16/17}{}{0}} \headcommand {\beamer@framepages {16}{17}} -\headcommand {\slideentry {0}{0}{8}{18/18}{}{0}} -\headcommand {\beamer@framepages {18}{18}} -\headcommand {\slideentry {0}{0}{9}{19/19}{}{0}} -\headcommand {\beamer@framepages {19}{19}} -\headcommand {\slideentry {0}{0}{10}{20/20}{}{0}} -\headcommand {\beamer@framepages {20}{20}} -\headcommand {\beamer@partpages {1}{20}} -\headcommand {\beamer@subsectionpages {1}{20}} -\headcommand {\beamer@sectionpages {1}{20}} -\headcommand {\beamer@documentpages {20}} -\headcommand {\def \inserttotalframenumber {10}} +\headcommand {\slideentry {0}{0}{7}{18/19}{}{0}} +\headcommand {\beamer@framepages {18}{19}} +\headcommand {\slideentry {0}{0}{8}{20/21}{}{0}} +\headcommand {\beamer@framepages {20}{21}} +\headcommand {\slideentry {0}{0}{9}{22/24}{}{0}} +\headcommand {\beamer@framepages {22}{24}} +\headcommand {\slideentry {0}{0}{10}{25/27}{}{0}} +\headcommand {\beamer@framepages {25}{27}} +\headcommand {\slideentry {0}{0}{11}{28/29}{}{0}} +\headcommand {\beamer@framepages {28}{29}} +\headcommand {\slideentry {0}{0}{12}{30/31}{}{0}} +\headcommand {\beamer@framepages {30}{31}} +\headcommand {\slideentry {0}{0}{13}{32/34}{}{0}} +\headcommand {\beamer@framepages {32}{34}} +\headcommand {\slideentry {0}{0}{14}{35/35}{}{0}} +\headcommand {\beamer@framepages {35}{35}} +\headcommand {\beamer@partpages {1}{35}} +\headcommand {\beamer@subsectionpages {1}{35}} +\headcommand {\beamer@sectionpages {1}{35}} +\headcommand {\beamer@documentpages {35}} +\headcommand {\def \inserttotalframenumber {14}} diff --git a/aps_mm_2017.pdf b/aps_mm_2017.pdf index fd007e7..4940523 100644 Binary files a/aps_mm_2017.pdf and b/aps_mm_2017.pdf differ diff --git a/aps_mm_2017.synctex.gz b/aps_mm_2017.synctex.gz index d487693..b1b88d8 100644 Binary files a/aps_mm_2017.synctex.gz and b/aps_mm_2017.synctex.gz differ diff --git a/aps_mm_2017.tex b/aps_mm_2017.tex index d7b0a7f..e85f277 100644 --- a/aps_mm_2017.tex +++ b/aps_mm_2017.tex @@ -34,6 +34,38 @@ \titlepage \end{frame} +\begin{frame} + \frametitle{Parametric Ising Models} + \begin{columns} + \begin{column}{0.4\textwidth} + \includegraphics[width=\textwidth]{figs/fig7} + + \vspace{1em} + + \includegraphics[width=\textwidth,height=0.5\textwidth]{susceptibility.jpg} + + \tiny\texttt{a plot of susceptibility with precision parametric fit and it + isn't + very good at the abrupt transition} + \end{column} + \begin{column}{0.6\textwidth} + Scaling forms of Ising variables that do well globally. + + \pause\vspace{1em} + + Incorporate the critical point in a natural way: + \begin{itemize} + \item singular scaling with the ``radial coordinate'' + \item analytic scaling with the ``angular coordinate'' + \end{itemize} + + \vspace{1em} \pause + + Typically do a very poor job near the abrupt transition at $H=0$. + \end{column} + \end{columns} +\end{frame} + \begin{frame} \frametitle{Renormalization and Universality} @@ -63,7 +95,7 @@ \vspace{1em}\pause - Not all nonanalytic behavior is singular! + Not all nonanalytic behavior are power laws! \end{column} \end{columns} \end{frame} @@ -73,16 +105,18 @@ \begin{columns} \begin{column}{0.3\textwidth} - \includegraphics[width=\textwidth]{figs/fig3} + \only<1-1>{\includegraphics[width=\textwidth]{figs/fig3}} + \only<2->{\includegraphics[width=\textwidth]{figs/fig4}} \vspace{1em} - \includegraphics[width=\textwidth]{figs/fig4} + \includegraphics[width=\textwidth]{figs/fig8} + \end{column} \begin{column}{0.7\textwidth} Consider an Ising-class model brought into a metastable state. - \vspace{1em} \pause + \vspace{1em} \pause\pause A domain of $N$ spins entering the stable phase causes a free energy change @@ -141,9 +175,9 @@ \Delta F_\crit\sim\Sigma\bigg(\frac{MH}{\Sigma}\bigg)^{-(d-1)} =X^{-(d-1)}\mathcal F(X) \] - for $X=h/t^{\beta\delta}$, and + for $X=h/t^{\beta\delta}$, and \[ - \im F=\mathcal I(X)e^{-\beta/X^{(d-1)}} + \im F=t^{2-\alpha}\mathcal I(X)e^{-\beta/X^{(d-1)}} \] \end{frame} @@ -181,49 +215,108 @@ \begin{frame} \frametitle{The Essential Singularity} - Results from field theory indicate that $\mathcal I(X)\propto X$ for $d=2$ - and small $X$, so that + Results from field theory indicate that $\mathcal I(X)\propto X+\mathcal + O(X^2)$ for $d=2$, so that \[ - \im F=AXe^{-\beta/X^{(d-1)}} + \im F=t^{2-\alpha}\big(AX+\mathcal O(X^2)\big)e^{-\beta/X^{(d-1)}} \] + \pause + + The resulting moments for $n>1$ are \[ - f_n=\frac{A\Gamma(n-1)}{\pi(-B)^{n-1}} + f_n=At^{2-\alpha}\frac{\Gamma(n-1)}{\pi(-B)^{n-1}} \] + \pause + Not a convergent series---the real part of $F$ for $H>0$ is also - nonanalytic. + nonanalytic! \end{frame} \begin{frame} \frametitle{The Essential Singularity} In two dimensions, the Cauchy integral does not converge, normalize with + $\lambda$, \[ F(X\,|\,\lambda)=\frac1\pi\int_{-\infty}^0\frac{\im F(X')}{X'-X}\frac1{1+(\lambda X')^2}\;\dd X' \] + \pause + + Exact result has form \[ \begin{aligned} - \frac{A}\pi - \frac{Xe^{B/X}\ei(-B/X)+\frac1\lambda\im(e^{-i\lambda B}(i+\lambda - X)(\pi+i\ei(i\lambda B)))}{1+(\lambda X)^2} + F(X\,|\,\lambda)&=\frac{A}\pi\frac1{1+(\lambda X)^2}\Big[ + Xe^{B/X}\ei(-B/X)\\ + &\qquad+\frac1\lambda\im(e^{-i\lambda B}(i+\lambda + X)(\pi+i\ei(i\lambda B)))\Big] \end{aligned} \] + \pause + + The Cauchy integral is only predictive for high moments. + +\end{frame} +\begin{frame} + \frametitle{The Essential Singularity} + + What about the susceptibility $\chi=\frac{\partial^2\!F}{\partial h^2}$? + + \pause \vspace{1em} + + Has a well-defined limit as $\lambda\to0$, simple functional form: \[ \chi=t^{-\gamma}\mathcal X(h/t^{\beta\delta}) \] + where the scaling function is \[ \mathcal X(X)=\frac A{\pi X^3}\big[(B-X)X+B^2e^{B/X}\ei(-B/X)\big] \] + + \centering + \includegraphics[width=0.6\textwidth]{figs/fig9} +\end{frame} + +\begin{frame} + \frametitle{The Essential Singularity} + + Two parameter fit to simulations yields $A=-0.0939(8)$, $B=5.45(6)$, close + agreement in limit of small $t$ and $H$! + + \vspace{1em} + + \only<1-1>{\includegraphics[width=\textwidth]{figs/fig6}} + \only<2-2>{\includegraphics[width=\textwidth]{figs/fig5}} + + \vspace{1em}\pause \end{frame} \begin{frame} - \includegraphics[width=0.8\textwidth]{figs/fig5} + \frametitle{What's Next} + + We have an explicit form for a new component of the universal scaling forms + near the Ising abrupt transition. - $A=-0.0939(8)$, $B=5.45(6)$. + \vspace{1em} \pause + + Hope to form a parametric scaling variables that include this, correct + leading + analytic corrections to scaling, and (maybe?) extend smoothly through the + metastable region. + + \vspace{1em} \pause + + Remain on the lookout for other universal properties to incorporate. +\end{frame} + +\begin{frame} + \huge + \centering + {\sl Questions?} \end{frame} \end{document} diff --git a/figs/fig7.pdf b/figs/fig7.pdf new file mode 100644 index 0000000..45bbe58 Binary files /dev/null and b/figs/fig7.pdf differ diff --git a/figs/fig8.pdf b/figs/fig8.pdf new file mode 100644 index 0000000..8ce799c Binary files /dev/null and b/figs/fig8.pdf differ diff --git a/figs/fig9.pdf b/figs/fig9.pdf new file mode 100644 index 0000000..4d94c8f Binary files /dev/null and b/figs/fig9.pdf differ -- cgit v1.2.3-70-g09d2