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-formula stuff
author
hackbard
<hackbard>
Fri, 23 May 2003 14:39:30 +0000
(14:39 +0000)
committer
hackbard
<hackbard>
Fri, 23 May 2003 14:39:30 +0000
(14:39 +0000)
ising/ising.tex
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diff --git
a/ising/ising.tex
b/ising/ising.tex
index
87bb894
..
a992985
100644
(file)
--- a/
ising/ising.tex
+++ b/
ising/ising.tex
@@
-237,9
+237,9
@@
Dabei wurde verwendet, dass $\lambda_+^N$ im thermodynamischen Limes viel groess
Fuer die Magnetisierung mit Magnetfeld gilt:
\[
\begin{array}{ll}
Fuer die Magnetisierung mit Magnetfeld gilt:
\[
\begin{array}{ll}
- \displaystyle M & = \frac{1}{Z} \sum_{\{S\}} (\sum_{i} \mu S_i) e^{-\beta H} \\[2mm]
- \displaystyle & = \frac{1}{\beta} (\frac{\partial}{\partial{B_0}} \, \textrm{ln} \, Z) \\[2mm]
- \displaystyle & \stackrel{N >> 1}{\longrightarrow} \frac{N}{\beta \lambda_+} \frac{\partial{\lambda_+}}{\partial{B_0}} \\[2mm]
+ \displaystyle M &
\displaystyle
= \frac{1}{Z} \sum_{\{S\}} (\sum_{i} \mu S_i) e^{-\beta H} \\[2mm]
+ \displaystyle &
\displaystyle
= \frac{1}{\beta} (\frac{\partial}{\partial{B_0}} \, \textrm{ln} \, Z) \\[2mm]
+ \displaystyle & \
displaystyle \
stackrel{N >> 1}{\longrightarrow} \frac{N}{\beta \lambda_+} \frac{\partial{\lambda_+}}{\partial{B_0}} \\[2mm]
\displaystyle & \displaystyle = N \mu \frac{\sinh (\beta \mu B_0)}{\sqrt{\cosh^2 (\beta \mu B_0) - 2e^{-2 \beta J} \sinh (2 \beta J)}}
\end{array}
\displaystyle & \displaystyle = N \mu \frac{\sinh (\beta \mu B_0)}{\sqrt{\cosh^2 (\beta \mu B_0) - 2e^{-2 \beta J} \sinh (2 \beta J)}}
\end{array}
@@
-341,7
+341,7
@@
Gesucht sei der Erwartungswert $<A>$.
\[
\begin{array}{l}
\displaystyle <A> = \sum_i p_i A_i \, \textrm{, wobei} \\[2mm]
\[
\begin{array}{l}
\displaystyle <A> = \sum_i p_i A_i \, \textrm{, wobei} \\[2mm]
- \displaystyle p_i = \frac{e^{- \beta E_i}}{\sum_j e^{\beta E_j}} \, \textrm{Boltzmann Wahrscheinlichkeitsverteilung} \\[2mm]
+ \displaystyle p_i = \frac{e^{- \beta E_i}}{\sum_j e^{\beta E_j}} \, \textrm{
,
Boltzmann Wahrscheinlichkeitsverteilung} \\[2mm]
\displaystyle E_i \, \textrm{Energie im Zustand i}
\end{array}
\]
\displaystyle E_i \, \textrm{Energie im Zustand i}
\end{array}
\]