\sect{Ising in interaction with lattice gas}
Consider a one dimensional Ising model of spins $\sigma_{i}=\pm1$
labeled $i=1,2,3,...,M$, with periodic boundary condition.
Between each two spins there is a site $n_i=0,1$ that can be occupied by an atom.
If the atom is present the feromagnetic coupling
is decreased from $J$ to $(1-\lambda)J$.
\Dn
(1) Evaluate the partition sum assuming that there
are $N$ atoms in the $M$ sites. Allow all configurations
of spins and of atoms. Calculate the free energy $F$.
\Dn
(2) If the atoms are stationary impurities one needs to evaluate the
free energy $F$ for some random configuration of the atoms.
What is the entropy difference between the results?
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