From 8e422e13d7ddcd89704668a0ccf688f2dfeea749 Mon Sep 17 00:00:00 2001
From: Alex Schmidt <alex@treefish.org>
Date: Thu, 24 Oct 2013 13:35:46 +0200
Subject: [PATCH] Ydalia: Modified a little bit the text and the plots
 plaquettes.eps and segments.eps. The problem is that the blue and red links
 look the same in the printed version :-(.  So I had to made the blue links
 fatter :-/ Also, I made the plots bigger since we have a couple of pages of
 extra space.

---
 pics/plaquettes-eps-converted-to.pdf | Bin 5476 -> 5476 bytes
 pics/plaquettes.eps                  | 177 ++++++++++++++-------------
 pics/segments-eps-converted-to.pdf   | Bin 5471 -> 5465 bytes
 pics/segments.eps                    |  51 ++++----
 proceed.tex                          |  25 ++--
 5 files changed, 132 insertions(+), 121 deletions(-)

diff --git a/pics/plaquettes-eps-converted-to.pdf b/pics/plaquettes-eps-converted-to.pdf
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diff --git a/pics/plaquettes.eps b/pics/plaquettes.eps
index b8917d2..aada480 100644
--- a/pics/plaquettes.eps
+++ b/pics/plaquettes.eps
@@ -1,8 +1,8 @@
 %!PS-Adobe-3.0 EPSF-3.0
 %%Title: plaquettes.fig
 %%Creator: fig2dev Version 3.2 Patchlevel 5d
-%%CreationDate: Tue Jul  9 14:10:29 2013
-%%BoundingBox: 0 0 719 108
+%%CreationDate: Thu Oct 24 13:01:56 2013
+%%BoundingBox: 0 0 721 108
 %Magnification: 1.0000
 %%EndComments
 %%BeginProlog
@@ -81,7 +81,7 @@ end
 
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 save
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diff --git a/pics/segments-eps-converted-to.pdf b/pics/segments-eps-converted-to.pdf
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diff --git a/pics/segments.eps b/pics/segments.eps
index 3300379..16f62ec 100644
--- a/pics/segments.eps
+++ b/pics/segments.eps
@@ -1,8 +1,8 @@
 %!PS-Adobe-3.0 EPSF-3.0
 %%Title: plaquettes.fig
 %%Creator: fig2dev Version 3.2 Patchlevel 5d
-%%CreationDate: Wed Oct 23 10:16:57 2013
-%%BoundingBox: 0 0 719 108
+%%CreationDate: Thu Oct 24 12:48:12 2013
+%%BoundingBox: 0 0 721 108
 %Magnification: 1.0000
 %%EndComments
 %%BeginProlog
@@ -81,7 +81,7 @@ end
 
 /pageheader {
 save
-newpath 0 108 moveto 0 0 lineto 719 0 lineto 719 108 lineto closepath clip newpath
+newpath 0 108 moveto 0 0 lineto 721 0 lineto 721 108 lineto closepath clip newpath
 -26.3 486.9 translate
 1 -1 scale
 $F2psBegin
@@ -153,6 +153,7 @@ n 6150 7425 m
 n 5700 6825 m
  7125 6825 l gs col19 s gr  [] 0 sd
 % Polyline
+75.000 slw
 n 8325 6825 m
  9750 6825 l gs col9 s gr 
 % Polyline
@@ -166,27 +167,6 @@ n 9900 7425 m
  10950 6825 l gs col-1 s gr  [] 0 sd
 % Polyline
 7.500 slw
-n 10200 7350 m 10950 6900 l 12150 6900 l 11400 7350 l
- cp gs col11 1.00 shd ef gr gs col0 s gr 
-% Polyline
-30.000 slw
-n 11400 7425 m
- 9900 7425 l gs col9 s gr 
-% Polyline
- [120] 0 sd
-n 10950 6825 m
- 12375 6825 l gs col9 s gr  [] 0 sd
-% Polyline
-7.500 slw
-gs  clippath
-11220 6988 m 11220 7140 l 11280 7140 l 11280 6988 l 11280 6988 l 11250 7108 l 11220 6988 l cp
-eoclip
-n 11250 6600 m
- 11250 7125 l gs col0 s gr gr
-
-% arrowhead
-n 11220 6988 m 11250 7108 l 11280 6988 l  col0 s
-% Polyline
 n 6000 6450 m
  6150 6450 l gs col0 s gr 
 % Polyline
@@ -213,6 +193,18 @@ n 6153 7429 m
  [15 90] 90 sd
 n 7275 7425 m
  8325 6825 l gs col-1 s gr  [] 0 sd
+% Polyline
+7.500 slw
+n 10200 7350 m 10950 6900 l 12150 6900 l 11400 7350 l
+ cp gs col11 1.00 shd ef gr gs col0 s gr 
+% Polyline
+75.000 slw
+n 11400 7425 m
+ 9900 7425 l gs col9 s gr 
+% Polyline
+ [120] 0 sd
+n 10950 6825 m
+ 12375 6825 l gs col9 s gr  [] 0 sd
 /Symbol ff 283.33 scf sf
 1500 7275 m
 gs 1 -1 sc (n) col0 sh gr
@@ -233,12 +225,21 @@ gs 1 -1 sc (+) col0 sh gr
 gs 1 -1 sc (+) col0 sh gr
 % here ends figure;
 % 
-% here starts figure with depth 45
+% here starts figure with depth 46
 % Polyline
 0 slj
 0 slc
 7.500 slw
 gs  clippath
+11220 6988 m 11220 7140 l 11280 7140 l 11280 6988 l 11280 6988 l 11250 7108 l 11220 6988 l cp
+eoclip
+n 11250 6600 m
+ 11250 7125 l gs col0 s gr gr
+
+% arrowhead
+n 11220 6988 m 11250 7108 l 11280 6988 l  col0 s
+% Polyline
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 5970 6988 m 5970 7140 l 6030 7140 l 6030 6988 l 6030 6988 l 6000 7108 l 5970 6988 l cp
 eoclip
 n 6000 6600 m
diff --git a/proceed.tex b/proceed.tex
index 12e7768..bef9b30 100644
--- a/proceed.tex
+++ b/proceed.tex
@@ -205,7 +205,8 @@ It consists of increasing or decreasing a plaquette occupation number
 $p_{x,\nu\rho}$ and
 the link fluxes (either $l_{x,\sigma}$ or $j_{x,\sigma}$) at the edges of $p_{x,\nu\rho}$ by $\pm 1$ as 
 illustrated in Fig.~\ref{plaquette}. The change of $p_{x, \nu \rho}$ 
-by $\pm 1$ is indicated by the signs $+$ or $-$, while the flux variables $l$($j$) are denoted by the red(blue) lines
+by $\pm 1$ is indicated by the signs $+$ or $-$, while the flux variables $l$($j$) are denoted by the thin red line
+(fat blue lines)
 and we use a dashed line to indicate a decrease by $-1$ and a full line for an increase by $+1$.
 %
 \vspace*{-1mm}
@@ -234,7 +235,7 @@ probability computed from the local weight factors.
 \end{center}
 \vspace{-4mm}
 \caption{Plaquette update: A plaquette occupation number is changed by $+1$ or
-$-1$ and the links $l$ (red) or $j$ (blue) of the plaquette are changed simultaneously. The
+$-1$ and the links $l$ (thin red links) or $j$ (fat blue links) of the plaquette are changed simultaneously. The
 full line indicates an increase by +1 and a dashed line a decrease by $-1$. 
 The directions $1 \le \nu_1 < \nu_2 \le 4$
 indicate the plane of the plaquette.} \label{plaquette}
@@ -337,10 +338,10 @@ n  = \frac{1}{N_s^3 N_t}\frac{\partial}{\partial \mu} \ln\ Z\quad , \quad
 \subsection{Algorithm assessment}
 \noindent
 For the comparison of both algorithms we considered the U(1) gauge-Higgs model coupled
-with two (as described above) and with only one scalar field \cite{swa}.  
+with one (see \cite{swa}) and two scalar fields (as described here).  
 First we checked the correctness of the SWA comparing the results for different 
 lattices sizes and parameters.  Examples for the one flavor model are shown in \cite{swa}.
-Fig.~\ref{obs} shows two observables for the two flavor case.
+In Fig.~\ref{obs} we can observe some examples for the two flavor case.
 The figure on the top shows 
 $\langle |\phi|^2 \rangle$ (lhs.) and its susceptibility (rhs.) as a function of $\mu$ 
 at $\beta = 0.85$ and $M^2 = 5.325$ on a lattice of size $12^3 \times 60$.  This point is located
@@ -356,7 +357,8 @@ We observe very good agreement between both algorithms.
 \hbox{\hspace{4mm}\includegraphics[width=0.97\textwidth,clip]{pics/bn}}
 \end{center}
 \vspace{-6mm}
-\caption{Observables as a function of $\mu$ for different parameters on a $12^3 \times 60$ lattice.
+\caption{Observables for the two flavor model as a function of $\mu$ for different 
+parameters on a $12^3 \times 60$ lattice.
 We compare results from the SWA (circles) and the LMA (triangles).} \label{obs}
 \vspace*{-2mm}
 \end{figure}
@@ -380,7 +382,7 @@ a sweep of cube updates.
 \end{center}
 \vspace{-4mm}
 \caption{Normalized autocorrelation times $\overline{\tau}$ for 2 different set
-of parameters.  Left: parameters close to a first order phase transition. 
+of parameters for the one flavor model.  Left: parameters close to a first order phase transition. 
 Right: low acceptance rate of the variable $l$.  Both simulations correspond
 to a $16^4$ lattice.  Data taken from \cite{swa}.} \label{auto}
 \vspace*{-2mm}
@@ -400,7 +402,7 @@ models \cite{Lang}.
 \begin{figure}[h]
 \centering
 \hspace*{-3mm}
-\includegraphics[width=75mm,clip]{pics/phasediagram}
+\includegraphics[width=85mm,clip]{pics/phasediagram}
 \caption{Phase diagram in the $\beta$-$M^2$ plane at $\mu = 0$. We show
 the phase boundaries determined from the maxima of the susceptibilities $\chi_U$ and $\chi_{\phi}$ and the
 inflection points of $\chi_n$.}
@@ -417,7 +419,7 @@ For all observables it can be seen that the phase-boundaries in general become m
 \begin{figure}[h]
 \centering
 \hspace*{-3mm}
-\includegraphics[width=130mm,clip]{pics/muphases}
+\includegraphics[width=\linewidth,clip]{pics/muphases}
 \caption{We show the observables $\langle U \rangle$, $\langle |\phi|^2 \rangle$, $\langle n \rangle$ as function of $\beta$ and $M^2$ for different $\mu = 0,0.5,1,1.5$. It can be seen how the phase boundaries change with increasing chemical potential.}
 \label{muphases}
 \end{figure}
@@ -431,19 +433,20 @@ In Fig.~\ref{occutrans_plaq} we plot the plaquette expectation value $\langle U
 $\langle U \rangle$ and $\chi_U$ are independent of $\mu$, which is characteristic for a Silverblaze type transition \cite{cohen}.
 
 \noindent
-Then in Fig.~\ref{occutrans} we show the occupation numbers of all dual link variables $\bar{j}$, $\bar{l}$, $j$, $l$ and dual plaquette variables $p$ just below (top) and above (bottom) the critical chemical potential $\mu_c$. Here blue links/plaquettes depict positive occupation numbers, green links/plaquettes depict negative occupation numbers and links/plaquettes with $0$-occupation are spared out. It can be seen that below $\mu_c$ links and plaquettes are hardly occupied, while above $\mu_c$ they are highly occupied. In that sense the Silverblaze transition shown in Fig.~\ref{occutrans_plaq} can be understood as condensation phenomenon, which is a new perspective on the underlying physics we gained from the dual reformulation of the problem.
+Then in Fig.~\ref{occutrans} we show the occupation numbers of all dual link variables $\bar{j}$, $\bar{l}$, $j$, 
+$l$ and dual plaquette variables $p$ just below (top) and above (bottom) the critical chemical potential $\mu_c$. Here blue links/plaquettes depict positive occupation numbers, green links/plaquettes depict negative occupation numbers and links/plaquettes with $0$-occupation are spared out. It can be seen that below $\mu_c$ links and plaquettes are hardly occupied, while above $\mu_c$ they are highly occupied. In that sense the Silverblaze transition shown in Fig.~\ref{occutrans_plaq} can be understood as condensation phenomenon, which is a new perspective on the underlying physics we gained from the dual reformulation of the problem.
 
 \begin{figure}[h]
 \centering
 \hspace*{-3mm}
-\includegraphics[width=130mm,clip]{pics/occutrans_plaq}
+\includegraphics[width=\linewidth,clip]{pics/occutrans_plaq}
 \caption{We here show the plaquette expectation value $\langle U \rangle$ and the corresponding suscpetibility $\chi_U$ as function of the chemical potential, for two different volumes $12^3\times60$ and $16^3\times60$.}
 \label{occutrans_plaq}
 \end{figure}
 \begin{figure}[h]
 \centering
 \hspace*{-3mm}
-\includegraphics[width=130mm,clip]{pics/occutrans}
+\includegraphics[width=\linewidth,clip]{pics/occutrans}
 \caption{Dual link occupation numbers $\bar{j}$, $\bar{l}$, $j$, $l$ and dual plaquette occupation numbers $p$ just below (top) and above (bottom) the transition from the confining- to the Higgs-phase shown in the previous plot.}
 \label{occutrans}
 \end{figure}
-- 
2.39.5