
\documentclass[portrait,a0]{a0poster}
%
\usepackage{etex}

\usepackage[svgnames]{xcolor}

\usepackage{color,colortbl,times,graphicx,multicol}
\usepackage{psboxit,epsfig,wrapfig,boxedminipage}
\usepackage[absolute]{textpos}
\usepackage{subfigure}
\usepackage{tikz,slashed}
\usepackage{enumitem}
\usepackage{multirow}
\usepackage{caption}
\renewcommand{\familydefault}{\sfdefault}

\usepackage{amsfonts}

\color{black}

%some mathpackages
\usepackage[intlimits]{amsmath}
\usepackage{amssymb}
% \usepackage{bbm}
\usepackage{mathrsfs}
% \usepackage{dsfont}
%allg. Symbole
\usepackage{wasysym}
%float figures
\usepackage{wrapfig}
\usepackage{url}
\usepackage[tight]{units}
\usepackage{ctable}

%\setlength{\textheight}{110.32cm}
\setlength{\textheight}{116.32cm}
\setlength{\textwidth}{76.96cm}
\setlength{\voffset}{-20mm}
\setlength{\hoffset}{-40mm}
%\setlength{\oddsidemargin}{5cm}
\setlength{\oddsidemargin}{5.5cm}

\setlength{\parindent}{0cm}

\newlength{\agrheight}
\newlength{\agrdoubleheight}
\setlength{\agrheight}{11cm}
\setlength{\agrdoubleheight}{18cm}

\newlength{\nontextsep}
\setlength{\nontextsep}{1cm}
\newlength{\agrsep}
\setlength{\agrsep}{2cm}
\newlength{\agrdoublesep}
\setlength{\agrdoublesep}{2cm}

% separation between columns
\setlength{\columnsep}{1.5cm}


% user defined commands
% own commands
\newcommand{\eq}[1]{(\ref{#1})}
\newcommand{\fig}[1]{Fig.~{\ref{#1}}}
\newcommand{\FC}{\;,}
\newcommand{\FD}{\;.}
\newcommand{\RD}[1]{{\mathrm{red}(#1)}}
\newcommand{\RDH}[1]{{\mathrm{red5}(#1)}}
\newcommand{\LM}[1]{{\mathrm{lm}(#1)}}
\newcommand{\LMH}[1]{{\mathrm{lm5}(#1)}}
\newcommand{\SU}[1]{\mathrm{SU}(#1)}
\newcommand{\U}[1]{\mathrm{U}(#1)}
\newcommand{\dbar}{\overline{d}}
\newcommand{\ubar}{\overline{u}}

\definecolor{WildStrawberry}{cmyk}{0,0.96,0.39,0} % important phrases
\definecolor{CornflowerBlue}{cmyk}{0.65,0.13,0,0.4} % accentuation2
\definecolor{CornflowerBlueDark}{cmyk}{0.65,0.13,0,0.6} % structure
\definecolor{CadetBlue}{cmyk}{0.62,0.57,0.23,0} % gluons
\definecolor{Peach}{cmyk}{0,0.70,0.70,0.35} % ghosts
\definecolor{BurntOrange}{cmyk}{0,0.51,1,0} % gh-g vertices
\definecolor{Red}{cmyk}{0,1,1,0} % integral measure
\definecolor{SkyBlue}{cmyk}{0.62,0,0.12,0.3} % IR exponent

\definecolor{kfug-yellow}{rgb}{1 0.85 0}

\definecolor{Blue}{cmyk}{1,1,0,0} 
\definecolor{Red}{cmyk}{0,1,1,0} 

\renewcommand{\refname}{\vspace{-1.5cm}}

\renewcommand\footnoterule{}
\renewcommand{\thefootnote}{\fnsymbol{footnote}}

%\usepackage{showframe}

\setlength{\parindent}{0em}		% Absatzeinrueckung erste Zeile
\setlength{\parskip}{0em}			% Absatzzwischenraum

\renewcommand{\baselinestretch}{1.1}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%% document %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}


\noindent
\hspace*{-36mm}
\includegraphics[scale=1.01,clip]{./hintergrund}


\vspace*{-1140mm}

\vspace{-45mm}
% \hfill \includegraphics[width=.1\textwidth]{../../figures/oeaw_logo}
\hfill 
\includegraphics[width=.2\textwidth]{./fwf-logo}
\hspace{-30mm}
%\vspace{-40mm}

%% Titel
\vspace*{10mm}
\begin{center}
\fcolorbox{white}{white}
{
  \begin{minipage}[b]{400mm}
    \begin{center}
      \vspace*{10mm}
       \Huge{\sf
	\textcolor{cyan}{\bf Condensation in two flavor scalar electrodynamics with non-degenerate quark masses}}\\[7mm]
	\Large{\bf{Alexander Schmidt} \sf{, Philippe de Forcrand, Christof Gattringer} \\ \sf{\large University of Graz}}\\\vspace{-1cm}
    \end{center}
   \vspace*{1cm}
  \end{minipage}
}
\end{center}


\vspace{1.5cm}

%%%%%%%%%%%%%%%%%%%%%%% 2 columns %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{multicols}{2}


%%%%%%%%%%%%%%%%%%%%%%% ACTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\large \centering{\textcolor{cyan}{\LARGE\sf The action}}

\vspace{1.0cm}

\begin{minipage}[b]{350mm}

  In the conventional notation the lattice action is given by (the lattice constant is set to $a=1$)

  \vspace{1cm}

  \begin{flushleft}
    \small
    {\color{cyan}Gauge field $U_{\vec{n},\mu}$} \quad 
    {\color{magenta}1st flavor Higgs field $\phi_{\vec{n}}^1$} \quad
    {\color{ForestGreen}2nd flavor Higgs field $\phi_{\vec{n}}^2$}
  \end{flushleft}
  \begin{eqnarray}
    S \hspace{0.1cm} & = & S_G[U] + S_H[U,\phi] \label{latac} \\ \nonumber \\
    S_G & = & -  \beta \sum_{\vec{n}} \sum_{\mu < \nu}  Re \; {\color{cyan}U_{\vec{n},\mu} \, U_{\vec{n} + \hat{\mu}, \nu} \, U_{\vec{n} + \hat{\nu}, \mu}^\star \, U_{\vec{n},\nu}^\star} 
    \\
    S_{H} & = & \sum_{\vec{n}}\! \Bigg[ \kappa^1 \mid \!\! {\color{magenta}\phi^1_{\vec{n}}} \!\! \mid^2
    + \lambda^1 \mid \!\! {\color{magenta}\phi^1_{\vec{n}}} \!\! \mid^4  
    + \kappa^2 \mid \!\! {\color{ForestGreen}\phi^2_{\vec{n}}} \!\! \mid^2
    + \lambda^2 \mid \!\! {\color{ForestGreen}\phi^2_{\vec{n}}} \!\! \mid^4 \Bigg ] \ \\
    &-& \sum_{\vec{n}}\! \Bigg[ \sum_{\mu}\! \Bigg( e^{\delta_{\mu 4} \mu^1}{\color{magenta}{\phi^1_{\vec{n}}}^\star} \, {\color{cyan}U_{\vec{n},\mu}} \,  {\color{magenta}\phi^1_{\vec{n}+\widehat{\mu}}}   
    + e^{-\delta_{\mu 4} \mu^1} {\color{magenta}{\phi^1_{\vec{n}}}^\star} \, {\color{cyan}U_{\vec{n} - \widehat{\mu},\mu}^\star} \,  {\color{magenta}\phi^1_{\vec{n}-\widehat{\mu}}} \Bigg) \Bigg] \nonumber \\
    &-& \sum_{\vec{n}}\! \Bigg[ \sum_{\mu}\! \Bigg( e^{\delta_{\mu 4} \mu^2}{\color{ForestGreen}{\phi^2_{\vec{n}}}^\star} \, {\color{cyan}U_{\vec{n},\mu}^\star} \,  {\color{ForestGreen}\phi^2_{\vec{n}+\widehat{\mu}}}   
    + e^{-\delta_{\mu 4} \mu^2} {\color{ForestGreen}{\phi^2_{\vec{n}}}^\star} \, {\color{cyan}U_{\vec{n} - \widehat{\mu},\mu}} \,  {\color{ForestGreen}\phi^2_{\vec{n}-\widehat{\mu}}} \Bigg) \Bigg]
    \nonumber
  \end{eqnarray}
  \begin{flushright}
    \small
    {\color{gray}$U_{\vec{n},\mu} \in U(1)$, $\phi_{\vec{n}} \in \mathbb{C}$}
  \end{flushright}


  \vspace{0.2cm}

  \vspace{0.2cm}

  with $\beta$ the inverse gauge coupling, $\kappa^i$ the effective masses and $\lambda^i$ the Higgs coupling constants.

  \vspace{-24pt}
\end{minipage}
\vspace{2.0cm}


%%%%%%%%%%%%%%%%%%%%%%% FLUX ACTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\large \centering{\textcolor{cyan}{\LARGE\sf Flux representation of the action}}

\vspace{1.0cm}

\begin{minipage}[b]{350mm}

  {\textcolor{cyan}{\Large\sf The basic idea}} 
  is to expand the partition sum and perform the summation over the original degrees of freedom.

  \vspace{0.5cm}

  {\textcolor{cyan}{\Large\sf As an example}} 
  we look at a single nearest neighbour term
  \begin{eqnarray}
    Z \; \propto \; e^{\phi_x^\star \, U_{x,\nu} \,\phi_{x+\widehat{\nu}}}
    \; = \; \sum_{k_{x,\mu}}    \frac{1}{ (k_{x,\mu})!} \; 
    \bigg[ \, \phi_x^\star \, U_{x,\nu} \,\phi_{x+\widehat{\nu}} \bigg]^{\, k_{x,\mu}} \quad .
    \nonumber
  \end{eqnarray}

  Performing the summation over $\phi^i$ our partition sum no longer depends on the fields $\phi^i$
  \begin{eqnarray*}
    Z \; = \; \sum_{\{\phi\}} \sum_{\{U\}} \; e^{-S_G(U)-S_H(U,\phi)} &=& \sum_{\{\phi\}} \sum_{\{U\}} \; e^{-S_G(U)} \sum_{\{k,l\}} F(U,\phi,k,l) \\
    &=& \sum_{\{k,l\}} \sum_{\{U\}} \; e^{-S_G(U)} \underbrace{\sum_{\{\phi\}} F(U,\phi,k,l)}_{\textnormal{perform this summation}} \quad .
  \end{eqnarray*}

  {\textcolor{cyan}{\Large\sf Finally}}
  we end up with a real and positive partition sum plus constraints for the dual degrees of freedom
  \begin{eqnarray*}
    Z \; = \; \sum_{\{k,l\}} \sum_{\{p\}} FB(k,l,p) = \hspace{-0.5cm} \sum_{\{p, k^1, l^1, k^2, l^2\}} \hspace{-0.5cm} {\cal W}(p,k,l) \, {\cal C}_B(p,k^1,k^2) \, {\cal C}_F(k^i) \quad .
  \end{eqnarray*}

  \vspace{0.2cm}

  %\begin{center}
    %\includegraphics[height=13cm]{dofs.pdf}
  %\end{center}

  \vspace{-24pt}
\end{minipage}
\vspace{2.0cm}


%%%%%%%%%%%%%%%%%%%%%%% PHASE DIAGRAM %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\large \centering{\textcolor{cyan}{\LARGE\sf Phase diagram}}

\vspace{1.0cm}

\begin{minipage}[b]{350mm}

  \begin{center}
    \includegraphics[height=25cm]{phasediagram.pdf}
    \cite{PhysRevLett.111.141601}
  \end{center}

  \vspace{-24pt}
\end{minipage}
\vspace{2.0cm}

%%%%%%%%%%%%%%%%%%%%%%% MASS CORRELATORS %%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\large \centering{\textcolor{cyan}{\LARGE\sf Mass correlators in the confined phase}}

\vspace{1.0cm}

\begin{minipage}[b]{350mm}

  For the fundamental correlators $F_1$ and $F_2$, as expected, we see no plateaus. The masses of the bound states $U_1$ and $U_2$ are split because we set the effective masses of the two flavours to different values.

  \begin{center}
    \includegraphics[height=28cm]{mass.pdf}
  \end{center}

  \vspace{-24pt}
\end{minipage}
\vspace{2.0cm}

%%%%%%%%%%%%%%%%%%%%%%% CONDENSATION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\large \centering{\textcolor{cyan}{\LARGE\sf Condensation}}

\vspace{1.0cm}

\begin{minipage}[b]{350mm}

  We here show different observables as function of $\mu$. The dotted lines show the masses $U_1$ and $U_1$ determined from the plots above.

  \begin{center}
    \includegraphics[height=35cm]{finmu_840.pdf}
  \end{center}

  \vspace{-24pt}
\end{minipage}
\vspace{2.0cm}

%%%%%%%%%%%%%%%%%%%%%%%%%% Acknowledgments %%%%%%%%%%%%%%%%%%%%%%%%%%%%

\hrule
\vspace{1.0cm}
\large \centering{\textcolor{cyan}{\Large\sf Acknowledgments}}

\vspace{1.0cm}

\begin{minipage}[b]{350mm}
This work was supported by the Austrian Science Fund, FWF, through the Doctoral
Program on {\it Hadrons in Vacuum, Nuclei, and Stars} (FWF DK W1203-N16).
\end{minipage}

%%%%%%%%%%%%%%%%%%%%%%%%%% References %%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\hrule
\vspace{1.7cm}
\large \centering{\textcolor{cyan}{\Large\sf References}}

\vspace{-1.0cm}

\begin{minipage}[b]{350mm}
    %\begin{multicols}{2}

      % \hrulefill
      \vspace{-8cm}
      \footnotesize
      \bibliographystyle{plain}
      \bibliography{bib}
      \vspace{-3cm}

    %\end{multicols}\vspace{-24pt}
  \end{minipage}

\end{multicols}
\end{document}
