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.
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$p_{x,\nu\rho}$ 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}
\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}
\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
\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}
\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}
\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 $\chi_n$.}
\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}
$\langle U \rangle$ 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}
projects / phys / proceedings_lattice13.git / commitdiff