Classical Limits of Euclidean Gibbs States for Quantum Lattice Models

Models of quantum and classical particles on a lattice ^d are considered. The classical model is obtained from the corresponding quantum model when the reduced mass of the particle m = / #x210F;² tends to infinity. For these models, the convergence of the Euclidean Gibbs states, when m + , is described in terms of the weak convergence of local Gibbs specifications, determined by conditional Gibbs measures. In fact, it is shown 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 pair interactions possessing the translation invariance, has also been shown.