From 330000dcacd34664b2baadbda8e4a4afb57e41ec Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 28 Feb 2017 18:00:01 -0500 Subject: changes made --- aps_mm_2017.aux | 37 + aps_mm_2017.log | 1349 ++++++++++++++++++++++++ aps_mm_2017.nav | 18 + aps_mm_2017.out | 0 aps_mm_2017.pdf | Bin 0 -> 88369 bytes aps_mm_2017.snm | 0 aps_mm_2017.synctex.gz | Bin 0 -> 12244 bytes aps_mm_2017.tex | 91 +- aps_mm_2017.toc | 1 + figs/fig1.pdf | Bin 0 -> 7095 bytes gen_figs.nb | 2706 ++++++++++++++++++++++++++++++++++++++++++++++++ 11 files changed, 4194 insertions(+), 8 deletions(-) create mode 100644 aps_mm_2017.aux create mode 100644 aps_mm_2017.log create mode 100644 aps_mm_2017.nav create mode 100644 aps_mm_2017.out create mode 100644 aps_mm_2017.pdf create mode 100644 aps_mm_2017.snm create mode 100644 aps_mm_2017.synctex.gz create mode 100644 aps_mm_2017.toc create mode 100644 figs/fig1.pdf create mode 100644 gen_figs.nb diff --git a/aps_mm_2017.aux b/aps_mm_2017.aux new file mode 100644 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335) + defining Unicode char U+0150 (decimal 336) + defining Unicode char U+0151 (decimal 337) + defining Unicode char U+0152 (decimal 338) + defining Unicode char U+0153 (decimal 339) + defining Unicode char U+0154 (decimal 340) + defining Unicode char U+0155 (decimal 341) + 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) + defining Unicode char U+015A (decimal 346) + 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) + defining Unicode char U+0162 (decimal 354) + defining Unicode char U+0163 (decimal 355) + defining Unicode char U+0164 (decimal 356) + defining Unicode char U+0165 (decimal 357) + defining Unicode char U+0168 (decimal 360) + defining Unicode char U+0169 (decimal 361) + 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) + defining Unicode char U+016E (decimal 366) + 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) + defining Unicode char U+0173 (decimal 371) + defining Unicode char U+0174 (decimal 372) + 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 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handling font encoding OT1 ... +... processing UTF-8 mapping file for font encoding OT1 + +(/usr/share/texmf-dist/tex/latex/base/ot1enc.dfu +File: ot1enc.dfu 2016/02/28 v1.1s UTF-8 support for inputenc + defining Unicode char U+00A0 (decimal 160) + defining Unicode char U+00A1 (decimal 161) + defining Unicode char U+00A3 (decimal 163) + defining Unicode char U+00AD (decimal 173) + defining Unicode char U+00B8 (decimal 184) + defining Unicode char U+00BF (decimal 191) + defining Unicode char U+00C5 (decimal 197) + defining Unicode char U+00C6 (decimal 198) + defining Unicode char U+00D8 (decimal 216) + defining Unicode char U+00DF (decimal 223) + defining Unicode char U+00E6 (decimal 230) + defining Unicode char U+00EC (decimal 236) + defining Unicode char U+00ED (decimal 237) + defining Unicode char U+00EE (decimal 238) + defining Unicode char U+00EF (decimal 239) + defining Unicode char U+00F8 (decimal 248) + defining Unicode char U+0131 (decimal 305) + defining Unicode char U+0141 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b/aps_mm_2017.synctex.gz differ 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} diff --git a/aps_mm_2017.toc b/aps_mm_2017.toc new file mode 100644 index 0000000..ae73954 --- /dev/null +++ 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