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-rw-r--r--aps_mm_2017.aux37
-rw-r--r--aps_mm_2017.log1349
-rw-r--r--aps_mm_2017.nav18
-rw-r--r--aps_mm_2017.out0
-rw-r--r--aps_mm_2017.pdfbin0 -> 88369 bytes
-rw-r--r--aps_mm_2017.snm0
-rw-r--r--aps_mm_2017.synctex.gzbin0 -> 12244 bytes
-rw-r--r--aps_mm_2017.tex91
-rw-r--r--aps_mm_2017.toc1
-rw-r--r--figs/fig1.pdfbin0 -> 7095 bytes
-rw-r--r--gen_figs.nb2706
11 files changed, 4194 insertions, 8 deletions
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+ defining Unicode char U+010B (decimal 267)
+ defining Unicode char U+010C (decimal 268)
+ defining Unicode char U+010D (decimal 269)
+ defining Unicode char U+010E (decimal 270)
+ defining Unicode char U+010F (decimal 271)
+ defining Unicode char U+0110 (decimal 272)
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+ defining Unicode char U+0117 (decimal 279)
+ defining Unicode char U+0118 (decimal 280)
+ defining Unicode char U+0119 (decimal 281)
+ defining Unicode char U+011A (decimal 282)
+ defining Unicode char U+011B (decimal 283)
+ defining Unicode char U+011C (decimal 284)
+ defining Unicode char U+011D (decimal 285)
+ defining Unicode char U+011E (decimal 286)
+ defining Unicode char U+011F (decimal 287)
+ defining Unicode char U+0120 (decimal 288)
+ defining Unicode char U+0121 (decimal 289)
+ defining Unicode char U+0122 (decimal 290)
+ defining Unicode char U+0123 (decimal 291)
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+ defining Unicode char U+012B (decimal 299)
+ defining Unicode char U+012C (decimal 300)
+ defining Unicode char U+012D (decimal 301)
+ defining Unicode char U+012E (decimal 302)
+ defining Unicode char U+012F (decimal 303)
+ defining Unicode char U+0130 (decimal 304)
+ defining Unicode char U+0131 (decimal 305)
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+ defining Unicode char U+013C (decimal 316)
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+ defining Unicode char U+013E (decimal 318)
+ defining Unicode char U+0141 (decimal 321)
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+ defining Unicode char U+0143 (decimal 323)
+ defining Unicode char U+0144 (decimal 324)
+ defining Unicode char U+0145 (decimal 325)
+ defining Unicode char U+0146 (decimal 326)
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+ defining Unicode char U+014A (decimal 330)
+ defining Unicode char U+014B (decimal 331)
+ defining Unicode char U+014C (decimal 332)
+ defining Unicode char U+014D (decimal 333)
+ defining Unicode char U+014E (decimal 334)
+ defining Unicode char U+014F (decimal 335)
+ defining Unicode char U+0150 (decimal 336)
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+ defining Unicode char U+0152 (decimal 338)
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+ defining Unicode char U+0156 (decimal 342)
+ defining Unicode char U+0157 (decimal 343)
+ defining Unicode char U+0158 (decimal 344)
+ defining Unicode char U+0159 (decimal 345)
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+ defining Unicode char U+015B (decimal 347)
+ defining Unicode char U+015C (decimal 348)
+ defining Unicode char U+015D (decimal 349)
+ defining Unicode char U+015E (decimal 350)
+ defining Unicode char U+015F (decimal 351)
+ defining Unicode char U+0160 (decimal 352)
+ defining Unicode char U+0161 (decimal 353)
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+ defining Unicode char U+0163 (decimal 355)
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+ defining Unicode char U+0165 (decimal 357)
+ defining Unicode char U+0168 (decimal 360)
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+ defining Unicode char U+016A (decimal 362)
+ defining Unicode char U+016B (decimal 363)
+ defining Unicode char U+016C (decimal 364)
+ defining Unicode char U+016D (decimal 365)
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+ defining Unicode char U+016F (decimal 367)
+ defining Unicode char U+0170 (decimal 368)
+ defining Unicode char U+0171 (decimal 369)
+ defining Unicode char U+0172 (decimal 370)
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+ defining Unicode char U+0175 (decimal 373)
+ defining Unicode char U+0176 (decimal 374)
+ defining Unicode char U+0177 (decimal 375)
+ defining Unicode char U+0178 (decimal 376)
+ defining Unicode char U+0179 (decimal 377)
+ defining Unicode char U+017A (decimal 378)
+ defining Unicode char U+017B (decimal 379)
+ defining Unicode char U+017C (decimal 380)
+ defining Unicode char U+017D (decimal 381)
+ defining Unicode char U+017E (decimal 382)
+ defining Unicode char U+01CD (decimal 461)
+ defining Unicode char U+01CE (decimal 462)
+ defining Unicode char U+01CF (decimal 463)
+ defining Unicode char U+01D0 (decimal 464)
+ defining Unicode char U+01D1 (decimal 465)
+ defining Unicode char U+01D2 (decimal 466)
+ defining Unicode char U+01D3 (decimal 467)
+ defining Unicode char U+01D4 (decimal 468)
+ defining Unicode char U+01E2 (decimal 482)
+ defining Unicode char U+01E3 (decimal 483)
+ defining Unicode char U+01E6 (decimal 486)
+ defining Unicode char U+01E7 (decimal 487)
+ defining Unicode char U+01E8 (decimal 488)
+ defining Unicode char U+01E9 (decimal 489)
+ defining Unicode char U+01EA (decimal 490)
+ defining Unicode char U+01EB (decimal 491)
+ defining Unicode char U+01F0 (decimal 496)
+ defining Unicode char U+01F4 (decimal 500)
+ defining Unicode char U+01F5 (decimal 501)
+ defining Unicode char U+0218 (decimal 536)
+ defining Unicode char U+0219 (decimal 537)
+ defining Unicode char U+021A (decimal 538)
+ defining Unicode char U+021B (decimal 539)
+ defining Unicode char U+1E02 (decimal 7682)
+ defining Unicode char U+1E03 (decimal 7683)
+ defining Unicode char U+200C (decimal 8204)
+ defining Unicode char U+2010 (decimal 8208)
+ defining Unicode char U+2011 (decimal 8209)
+ defining Unicode char U+2012 (decimal 8210)
+ defining Unicode char U+2013 (decimal 8211)
+ defining Unicode char U+2014 (decimal 8212)
+ defining Unicode char U+2015 (decimal 8213)
+ defining Unicode char U+2018 (decimal 8216)
+ defining Unicode char U+2019 (decimal 8217)
+ defining Unicode char U+201A (decimal 8218)
+ defining Unicode char U+201C (decimal 8220)
+ defining Unicode char U+201D (decimal 8221)
+ defining Unicode char U+201E (decimal 8222)
+ defining Unicode char U+2030 (decimal 8240)
+ defining Unicode char U+2031 (decimal 8241)
+ defining Unicode char U+2039 (decimal 8249)
+ defining Unicode char U+203A (decimal 8250)
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+ defining Unicode char U+00C6 (decimal 198)
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% 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}
diff --git a/aps_mm_2017.toc b/aps_mm_2017.toc
new file mode 100644
index 0000000..ae73954
--- /dev/null
+++ b/aps_mm_2017.toc
@@ -0,0 +1 @@
+\beamer@endinputifotherversion {3.36pt}
diff --git a/figs/fig1.pdf b/figs/fig1.pdf
new file mode 100644
index 0000000..2ecae6b
--- /dev/null
+++ b/figs/fig1.pdf
Binary files differ
diff --git a/gen_figs.nb b/gen_figs.nb
new file mode 100644
index 0000000..4d49987
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