\sect{Baruch's  C22.}

Consider the Ising model in one dimension with periodic boundary
condition and with zero external field.
\begin{itemize}
\item [(a)]
Consider an Ising spin ${\sigma_{i}\,\, ( \sigma_{i}=\pm 1)}$ at
site ${i}$ and explain why do you expect ${ \langle
\sigma_{i}\rangle=0}$ at any temperature ${T\neq 0}$. Evaluate
${\langle\sigma_{ i}\rangle}$ by using the transfer matrix method.
What is ${\langle\sigma_{ i}\rangle}$ at ${T=0}$?
\item [(b)]
Find the correlation function ${G\left(r\right)=\langle\sigma_{
1}\sigma_{ r+1}\rangle}$ and show that when ${N\rightarrow
\infty}$ (${N}$ is the number of spins) ${G\left(r\right)}$ has
the form $G\left(r\right)\sim e^{- r/\xi}$ . At what
temperature $\xi$ diverges and what is its significance?\\

\end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%