98-671 Sergio Albeverio, Yuri Kondratiev, Yuri Kozitsky

Classical Limits of Euclidean Gibbs States for Quantum Lattice Models (48K, LaTeX) Oct 22, 98

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Abstract. Models of quantum and classical particles on the $d$--dimensional lattice $\Zd$ with pair and many--particle interactions of a general type are considered. The classical model is obtained from the corresponding quantum one when the reduced physical mass of the particle $m = \mu /\hbar^2 $ tends to infinity. For these models, it is proved that in the case of pair interactions every net of quantum conditional Gibbs measures weakly converges to a classical conditional Gibbs measure when $m$ tends to infinity. In the case of general type interactions, it is proved that every conditional Gibbs measure of the classical model may be obtained as a weak limit of corresponding conditional Gibbs measures of the quantum model. The convergence of the probability kernels and periodic Gibbs measures for such models has also been proven. The latter convergence is then used to show the convergence of the order parameters which describe the phase transitions in the translation invariant models with pair interactions of the type cosidered.

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