From 330000dcacd34664b2baadbda8e4a4afb57e41ec Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 28 Feb 2017 18:00:01 -0500
Subject: changes made

---
 aps_mm_2017.tex | 91 ++++++++++++++++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 83 insertions(+), 8 deletions(-)

(limited to 'aps_mm_2017.tex')

diff --git a/aps_mm_2017.tex b/aps_mm_2017.tex
index 47f5e77..eda12da 100644
--- a/aps_mm_2017.tex
+++ b/aps_mm_2017.tex
@@ -5,33 +5,108 @@
 %  Copyright (c) 2012 pants productions. All rights reserved.
 %
 
-\pdfminorversion=4
 \documentclass[fleqn]{beamer}
 
 \usepackage[utf8]{inputenc}
+\usepackage{amsmath,amssymb,latexsym,graphicx}
+\usepackage{concmath}
+%\usepackage{bera}
+%\usepackage{merriweather}
 \usepackage[T1]{fontenc}
-\usepackage[scaled]{helvet}
-\usepackage{amsmath,amssymb,latexsym,graphicx,soul,amsthm,rotating,etex,sansmath,listings,tabularx,tikz}
-\usepackage[export]{adjustbox}
-\usecolortheme{beaver}
-\usetikzlibrary{decorations.pathreplacing}
 
+\usecolortheme{beaver}
+\usefonttheme{serif}
 
 \title{Universal scaling and the essential singularity at the Ising first-order transition}
 \author{ Jaron~Kent-Dobias\inst{1} \and James~Sethna\inst{1}}
 \institute{\inst{1}Cornell University}
 \date{16 March 2016}
 
-\usepackage[normalem]{ulem}
 \begin{document}
 
 \def\dd{\mathrm d}
+\def\im{\mathop{\mathrm{Im}}}
 
 \begin{frame}
-	\usefont{T1}{phv}{b}{n}
 	\titlepage
 \end{frame}
 
+\begin{frame}
+	\frametitle{Renormalization and free energy}
+	Rescale a system by a factor $b$, with couplings $K\to K'$.
+	From John Cardy's \emph{Scaling and Renormalization in Statistical Physics},
+	free energy per site $f$
+	\[
+		f(\{K\})=g(\{K\})+b^{-d}f(\{K'\})
+	\]
+	\begin{quote}
+		However, if we are interested in extracting only the \emph{singular}
+		behavior of $f$, \dots we may obtain a \emph{homogeneous} transformation law for the
+		\emph{singular part} of the free energy $f_s$
+		\[
+			f_s(\{K\})=b^{-d}f_s(\{K'\})
+		\]
+	\end{quote}
+	Defense: $g(\{K\})$ is an analytic function of $\{K\}$, while the singular
+	part is nonanalytic
+\end{frame}
+
+\begin{frame}
+	Follow thermodynamic functions onto metastable branch.
+\end{frame}
+
+\begin{frame}
+	\[\Delta f\sim\Sigma\gamma(N)-HMN\]
+	Near the critical point, $\gamma(N)\sim N^{\frac{d-1}d}$ 
+	\[
+		M=|t|^\beta\mathcal M(h/{t^{\beta\delta}})
+	\]
+	\[
+		N_{crit}\sim\bigg(\frac{\Sigma}{HM}\Big(1-\tfrac1d\Big)\bigg)^d
+	\]
+	\[
+		\Delta f_{crit}\sim\Sigma\bigg(\frac{\Sigma}{HM}\bigg)^{d-1}
+		\sim X^{-(d-1)}\frac{\mathcal
+		S^d(X)}{\mathcal M^{d-1}(X)}
+	\]
+	$X=h/t^{\beta\delta}$
+	The probability that such a domain forms and the metastable state decays is given by the Boltzmann factor,
+	so that
+	$\Sigma\sim|t|^\mu$, $\mu=-\nu+\gamma+2\beta$
+	\[
+		\im f\sim e^{-\beta\, \Delta f_{crit}}
+		\sim\mathcal F(X)e^{-1/X^{d-1}}
+	\]
+\end{frame}
+
+\begin{frame}
+	$e^{-1/x}$ is nonanalytic at $x=0$: all derivatives vanish, means that free
+	energy (which has no imaginary part in stable phase) is smooth
+
+	\centering
+	\includegraphics[width=0.7\textwidth]{figs/fig1}
+\end{frame}
+\begin{frame}
+	Analyticity of $F$ means that the imaginary
+
+	\[
+		f(h)=\sum_n A_nh^N
+	\]
+	\[
+		A_n=(-B)^{1-n}\Gamma(n-1)
+	\]
+
+	\[
+		f(h)=\frac1\pi\int_{h'<0}\frac{\dd h'\,\im f(h')}{h'-h}
+	\]
+\end{frame}
+
+\begin{frame}
+	Field theorists (Lubensky, blah blah blah)
+	\[
+		\mathcal
+	\]
+\end{frame}
 
 \end{document}
 
-- 
cgit v1.2.3-54-g00ecf

