somefixes

diff --git a/ising/ising_slides.tex b/ising/ising_slides.tex
index acd4553143492fe203bf58d4059b7736e46d8fbc..29a79263ba9d8f97208bce6eb4c04e872f2e3894 100644 (file)
--- a/ising/ising_slides.tex
+++ b/ising/ising_slides.tex
@@ -128,7 +128,10 @@ Molekularfeldn"aherung:\\
 Approximation: Vernachl"assigung der Spinfluktuationen $S_i-<S_i>$\\
 Spin-Wechselwirkungs-Term:
 \[
- S_iS_j = (S_i-m+m)(S_j-m+m)=m^2+m(S_i-m)+m(S_j-m)+(S_i-m)(S_j-m)
+\begin{array}{ll}
+ S_iS_j & = (S_i-m+m)(S_j-m+m)\\
+        & = m^2+m(S_i-m)+m(S_j-m)+(S_i-m)(S_j-m)
+\end{array}
 \]
 wobei:
 \begin{itemize}
@@ -282,7 +285,7 @@ Die Matrix muss also wie folgt aussehen:
 Zustandssumme:
 \[
  \begin{array}{ll}
- \displaystyle Z & \displaystyle = \sum_{S_1} \sum_{S_2} \ldots \sum_{S_N} <S_1|\mathbf{T}|S_2> <S_2|\mathbf{T}|S_3> \ldots <S_{N-1}|\mathbf{T}|S_N> <S_N|\mathbf{T}|S_1> \\[2mm]
+ \displaystyle Z & \displaystyle = \sum_{S_1} \sum_{S_2} \ldots \sum_{S_N} <S_1|\mathbf{T}|S_2> <S_2|\mathbf{T}|S_3> \ldots <S_N|\mathbf{T}|S_1> \\[2mm]
  \displaystyle  & \displaystyle = \sum_{S_1} <S_1|\mathbf{T}^N|S_1> \\[2mm]
  \displaystyle  & \displaystyle = \textrm{Sp} \, \mathbf{T}^N
  \end{array}
@@ -349,7 +352,7 @@ Erkenntnis:
 \end{itemize}
 F"ur $T=0$:
 \[ 
- \lim_{T \rightarrow 0} \frac{\lambda_+}{\lambda_-}=1 \, \textrm{obere Approximation nichtmehr g"ultig)}
+ \lim_{T \rightarrow 0} \frac{\lambda_+}{\lambda_-}=1 \, \textrm{, ist obere Approximation nichtmehr g"ultig}
 \]
 Phasen"ubergang bei $B_0=T=0$ (Korrelationsl"ange geht gegen unendlich)\\
 Kritische Exponenten:
@@ -497,7 +500,7 @@ somit gilt:
 
 \begin{slide}
 Realisierung einer Boltzmannverteilung: Metropolis Algorithmus\\
-$[4]$ http://www.npac.syr.edu/users/gcf/slitex/CPS713MonteCarlo96/index.html
+$[4]$ http://www.npac.syr.edu/users/gcf/slitex/CPS713MonteCarlo96/
 \[
  W(A \rightarrow B) = \left\{
  \begin{array}{ll}
@@ -608,7 +611,7 @@ Spingl"aser: Optimierung und Ged"achtnis
 \item \label{lit1} W. Nolting, Grundkurs: Statistische Physik, Band 6
 \item \label{lit2} Rodney J. Baxter, Exactly Solved Models in Statistical Mechanics
 \item \label{lit3} http://www.nyu.edu/classes/tuckerman/stat.mech/lectures/lecture\_26/node2.html
-\item \label{lit4} http://www.npac.syr.edu/users/gcf/slitex/CPS713MonteCarlo96/index.html
+\item \label{lit4} http://www.npac.syr.edu/users/gcf/slitex/CPS713MonteCarlo96/
 \item \label{lit5} Hildegard Meyer-Ortmanns, Abstract: Immigration, integration and ghetto formation
 \item \label{lit6} K. Malarz, Abstract: Social phase transition in Solomon network
 \item \label{lit7} Kerson Huang, Statistical mechanics