  We continue the study of the free energy of quantum lattice spin systems
where to the local Hamiltonian $H$ an arbitrary mean field term is added, a
polynomial function of the arithmetic mean of some local observables $X$ and
$Y$ that do not necessarily commute. By slightly extending a recent paper by
Hiai, Mosonyi, Ohno and Petz [9], we prove in general that the free energy is
given by a variational principle over the range of the operators $X$ and $Y$.
As in [9], the result is a noncommutative extension of the Laplace-Varadhan
asymptotic formula.
