Almost all corrections suggested by Philippe.

[phys/poster_lattice14.git] / poster_lattice14.tex

diff --git a/poster_lattice14.tex b/poster_lattice14.tex
index 8b5823f8bb85968dfd4b7f2ea84743e35483a7ff..837ca9ed7d0b99ea631c06778cf2f64a4d2b5211 100644 (file)
--- a/poster_lattice14.tex
+++ b/poster_lattice14.tex
@@ -222,7 +222,7 @@
 \begin{minipage}[b]{350mm}
 
   {\textcolor{cyan}{\Large\sf The basic idea}} 
 \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.
+  is to expand the partition sum and perform the integral over the original degrees of freedom.

 
   \vspace{0.5cm}
 
 
   \vspace{0.5cm}
 


@@ -232,20 +232,19 @@
     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 .
     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}
 
   \end{eqnarray}
 

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

 
   \vspace{0.2cm}
 
 
   \vspace{0.2cm}
 


@@ -305,8 +304,7 @@
 
 \begin{minipage}[b]{350mm}
 
 
 \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.
-
+  We here show different observables as function of $\mu=\mu_1=\mu_2$. The dotted lines show the masses $U_1$ and $U_2$ determined from the plots above. For the observables $\langle\phi^*\phi\rangle$ and $\langle n \rangle$ red symbols belong to flavor 1 and green symbols to flavor 2. 

   \begin{center}
     \includegraphics[height=35.8cm]{finmu_840.pdf}
   \end{center}
   \begin{center}
     \includegraphics[height=35.8cm]{finmu_840.pdf}
   \end{center}