more changes! very unfinished

author: Jaron Kent-Dobias <jaron@kent-dobias.com> 2017-03-10 01:23:36 -0500
committer: Jaron Kent-Dobias <jaron@kent-dobias.com> 2017-03-10 01:23:36 -0500
commit: 828ae03eb71aa24b0a1fda13f02684a3df3202eb (patch)
tree: 96a96816d90eb3bbceaf953b65ea0a5430b67ed1
parent: 1399f7eea0d4cc4ad16a9ac1b97dda445cbdfba0 (diff)
download: aps_mm_2017-828ae03eb71aa24b0a1fda13f02684a3df3202eb.tar.gz
aps_mm_2017-828ae03eb71aa24b0a1fda13f02684a3df3202eb.tar.bz2
aps_mm_2017-828ae03eb71aa24b0a1fda13f02684a3df3202eb.zip
14 files changed, 23008 insertions, 1028 deletions
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diff --git a/aps_mm_2017.pdf b/aps_mm_2017.pdf
index 4940523..76e69ca 100644
--- a/aps_mm_2017.pdf
+++ b/aps_mm_2017.pdf
diff --git a/aps_mm_2017.synctex.gz b/aps_mm_2017.synctex.gz
index b1b88d8..7c38fdf 100644
--- a/aps_mm_2017.synctex.gz
+++ b/aps_mm_2017.synctex.gz
diff --git a/aps_mm_2017.tex b/aps_mm_2017.tex
index e85f277..89f54ed 100644
--- a/aps_mm_2017.tex
+++ b/aps_mm_2017.tex
@@ -5,7 +5,7 @@
 %  Copyright (c) 2012 pants productions. All rights reserved.
 %
 
-\documentclass[fleqn]{beamer}
+\documentclass[fleqn,aspectratio=169]{beamer}
 
 \usepackage[utf8]{inputenc}
 \usepackage{amsmath,amssymb,latexsym,graphicx}
@@ -19,9 +19,9 @@
 \setbeamertemplate{navigation symbols}{}
 
 \title{Universal scaling and the essential singularity at the abrupt Ising transition}
-\author{ Jaron~Kent-Dobias\inst{1} \and James~Sethna\inst{1}}
-\institute{\inst{1}Cornell University}
-\date{16 March 2016}
+\author{ Jaron~Kent-Dobias \and James~Sethna}
+\institute{Cornell University}
+\date{16 March 2017}
 
 \begin{document}
 
@@ -35,107 +35,116 @@
 \end{frame}
 
 \begin{frame}
-  \frametitle{Parametric Ising Models}
+  \frametitle{Outline}
+  \begin{itemize}
+    \item Renormalization and the Ising model
+      \pause
+    \item Metastability and complex free energy
+      \pause
+    \item Analytic constraints on the stable free energy
+      \pause
+    \item Closed-form results for the {\sc 2d} Ising susceptibility 
+  \end{itemize}
+  \vfill
+\end{frame}
+
+\begin{frame}
+  \frametitle{Renormalization and the Ising Model}
   \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}
+      \centering 
+      \includegraphics[width=\textwidth]{figs/fig2}\\
+      \tiny
+      From \emph{Scaling and Renormalization in Statistical Physics} by John
+      Cardy
     \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 $H=0$.
+      {\sc Rg} analytically maps system space onto itself.
+      \vspace{1em}\pause\\
+      Fixed points correspond to phases, criticality.
+      \vspace{1em}\pause\\
+      Nonanalytic behavior is preserved by {\sc rg}.
     \end{column}
   \end{columns}
 \end{frame}
 
 \begin{frame}
-  \frametitle{Renormalization and Universality}
-
+  \frametitle{Renormalization and the Ising Model}
   \begin{columns}
     \begin{column}{0.4\textwidth}
-      \centering 
-      \includegraphics[width=\textwidth]{figs/fig2}
-
-      \tiny
-      From \emph{Scaling and Renormalization in Statistical Physics} by John
-      Cardy
+      \includegraphics{figs/fig3}
     \end{column}
     \begin{column}{0.6\textwidth}
-      Renormalization is an analytic scaling transformation that acts on
-      system space.
-
-      \vspace{1em}\pause
-
-      Fixed points are scale invariant, corresponding to systems representing
-      idealized phases or critical behavior.
-
-      \vspace{1em}\pause
-
-      Nonanalytic behavior---like power laws and logarithms---are preserved
-      under {\sc rg} and shared by \emph{any} system that flows to the same
-      point.
-
-      \vspace{1em}\pause
-
-      Not all nonanalytic behavior are power laws!
+      Ising critical point has power laws, logarithms in thermodynamic
+      variables.
+      \vspace{1em}\pause\\
+      Connected to line of abrupt transitions.
+      \vspace{1em}\pause\\
+      We've identified nonanalytic behavior along the abrupt transition line.
     \end{column}
   \end{columns}
 \end{frame}
 
 \begin{frame}
-  \frametitle{The Metastable Ising Model}
-
+  \frametitle{Metastability \& Complex Free Energy}
   \begin{columns}
-    \begin{column}{0.3\textwidth}
-      \only<1-1>{\includegraphics[width=\textwidth]{figs/fig3}}
-      \only<2->{\includegraphics[width=\textwidth]{figs/fig4}}
-
-      \vspace{1em}
-
-      \includegraphics[width=\textwidth]{figs/fig8}
-
+    \begin{column}{0.4\textwidth}
+      \includegraphics{figs/fig11}
     \end{column}
-    \begin{column}{0.7\textwidth}
-      Consider an Ising-class model brought into a metastable state.
-
-      \vspace{1em} \pause\pause
-
-      A domain of $N$ spins entering the stable phase causes a free energy
-      change
-      \[
-        \Delta F=\Sigma N^\sigma-MHN
-      \]
+    \begin{column}{0.6\textwidth}
+      \includegraphics{figs/fig12}
+    \end{column}
+  \end{columns}
+\end{frame}
 
-      \pause
+\begin{frame}
+  \frametitle{Metastability \& Complex Free Energy}
+  \begin{columns}
+    \begin{column}{0.4\textwidth}
+      \includegraphics{figs/fig13}
+    \end{column}
+    \begin{column}{0.6\textwidth}
+      \includegraphics{figs/fig14}
+    \end{column}
+  \end{columns}
+\end{frame}
 
-      The metastable phase is stable to domains smaller than
-      \[
-        N_\crit=\bigg(\frac{MH}{\sigma\Sigma}\bigg)^{-1/(\sigma-1)}
-      \]
-      but those larger will grow to occupy the entire system.
+\begin{frame}
+  \frametitle{Metastability \& Complex Free Energy}
+  \begin{columns}
+    \begin{column}{0.4\textwidth}
+      \includegraphics{figs/fig4}
+    \end{column}
+    \begin{column}{0.6\textwidth}
+      Thermodynamics can be continued into metastable phase.
+      \vspace{1em}\pause\\
+      Decay rate related to imaginary free energy,
+      $\Gamma\propto\frac1{kT}\im F$ (Langer 1969).
+      \vspace{1em}\pause\\
+      Ising metastable decay somewhat well studied (G\"unther 1980, Houghton
+      1980)
     \end{column}
   \end{columns}
 \end{frame}
 
 \begin{frame}
+  \frametitle{Metastability \& Complex Free Energy}
+  Decay of metastable phase occurs when domain of critical size forms.
+  \vspace{1em}\pause\\
+  Domain of $N$ spins entering the stable phase causes a free energy
+  change
+  \[
+    \Delta F=\Sigma N^\sigma-MHN
+  \]
+  \pause
+  Metastable phase is stable to domains smaller than
+  \[
+    N_\crit=\bigg(\frac{MH}{\sigma\Sigma}\bigg)^{-1/(\sigma-1)}
+  \]
+  but larger will grow to occupy the entire system, decay to stable phase.
+\end{frame}
+
+\begin{frame}
   \frametitle{The Metastable Ising Model}
 
   The formation of a critical domain has energy cost
diff --git a/figs/fig11.pdf b/figs/fig11.pdf
new file mode 100644
index 0000000..d15e8c9
--- /dev/null
+++ b/figs/fig11.pdf
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new file mode 100644
index 0000000..e519fad
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+++ b/figs/fig12.pdf
diff --git a/figs/fig13.pdf b/figs/fig13.pdf
new file mode 100644
index 0000000..73cd23e
--- /dev/null
+++ b/figs/fig13.pdf
diff --git a/figs/fig14.pdf b/figs/fig14.pdf
new file mode 100644
index 0000000..b0619bf
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+  " ", "\<\"Inverse functions are being used by \[NoBreak]\\!\\(Solve\\)\
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-(* End of internal cache information *)
author	Jaron Kent-Dobias <jaron@kent-dobias.com>	2017-03-10 01:23:36 -0500
committer	Jaron Kent-Dobias <jaron@kent-dobias.com>	2017-03-10 01:23:36 -0500
commit	828ae03eb71aa24b0a1fda13f02684a3df3202eb (patch)
tree	96a96816d90eb3bbceaf953b65ea0a5430b67ed1
parent	1399f7eea0d4cc4ad16a9ac1b97dda445cbdfba0 (diff)
download	aps_mm_2017-828ae03eb71aa24b0a1fda13f02684a3df3202eb.tar.gz aps_mm_2017-828ae03eb71aa24b0a1fda13f02684a3df3202eb.tar.bz2 aps_mm_2017-828ae03eb71aa24b0a1fda13f02684a3df3202eb.zip