  We find the free-energy in the thermodynamic limit of a one dimensional XY
model associated to a system of N qubits. The coupling among the sigma_i^z is a
long range two bodies random interaction. The randomness in the couplings is
the typical interaction of the Hopfield model with p patterns (p<<N), with the
patterns being p sequences of independent identically distributed (i.i.d.)
random variables assuming values \pm 1 with probability 1/2. We show also that
in the case p < alpha N the free-energy is asymptotically independent from the
choice of the patterns, i.e. it is self-averaging. The Hamiltonian is the one
used by (Neigovzen et al. 2009) in their experiment.
