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somefixes
author
hackbard
<hackbard>
Mon, 26 May 2003 17:23:04 +0000
(17:23 +0000)
committer
hackbard
<hackbard>
Mon, 26 May 2003 17:23:04 +0000
(17:23 +0000)
ising/ising_slides.tex
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diff --git
a/ising/ising_slides.tex
b/ising/ising_slides.tex
index
acd4553
..
29a7926
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:
\[
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}
\]
wobei:
\begin{itemize}
@@
-282,7
+285,7
@@
Die Matrix muss also wie folgt aussehen:
Zustandssumme:
\[
\begin{array}{ll}
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}
\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 $T=0$:
\[
\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:
\]
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\\
\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}
\[
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{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
\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