**
Below is the ascii version of the abstract for 04-119.
The html version should be ready soon.**Sergio Albeverio, Yuri kondratiev, Agnieszka Kozak, Yuri Kozitsky
A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence
(390K, pdf)
ABSTRACT. A hierarchical model of interacting quantum particles performing
anharmonic oscillations
is studied in the Euclidean approach, in which the local Gibbs states are constructed as measures on infinite
dimensional spaces. The local states restricted to the subalgebra generated by fluctuations of displacements of
particles are in the center of the study. They are described by means of the corresponding temperature Green
(Matsubara) functions. The result of the paper is a theorem, which describes the critical point convergence of such
Matsubara functions in the thermodynamic limit.