\sect{Ising model 1D, domain walls}
Consider the one dimensional Ising model with the Hamiltonian
${\cal H}=-\sum_{n,n'}J(n-n')\sigma(n)\sigma(n')$ with
$\sigma(n)=\pm 1$ at each site $n$,
and long range interaction $J(n)=b/n^{\gamma}$ with $b>0$.
Find the energy of a domain wall at $n=0$,
i.e. all the $n<0$ spins are "down" and the others are "up".
Show that the standard argument for the absence of spontaneous
magnetization at finite temperatures fails if ${\gamma <2}$.
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