Models of quantum and classical particles on the d-dimensional cubic lattice
with pair interparticle interactions are considered. The classical model is
obtained from the corresponding quantum one when the reduced physical mass of
the particle tends to infinity. For these models, it is proposed to define the
convergence of the Euclidean Gibbs states, when the reduced mass tends to
infinity, by the weak convergence of the corresponding Gibbs specifications,
determined by conditional Gibbs measures. In fact it is proved that all
conditional Gibbs measures of the quantum model weakly converge to the
conditional Gibbs measures of the classical model. A similar convergence of the
periodic Gibbs measures and, as a result, of the order parameters, for such
models with the pair interactions possessing the translation invariance, has
also been proven.