  A rigorous description of the equilibrium thermodynamic properties of an
infinite system of interacting $\nu$-dimensional quantum anharmonic oscillators
is given. The oscillators are indexed by the elements of a countable set
$\mathbb{L}\subset \mathbb{R}^d$, possibly irregular; the anharmonic potentials
vary from site to site. The description is based on the representation of the
Gibbs states in terms of path measures -- the so called Euclidean Gibbs
measures. It is proven that: (a) the set of such measures $\mathcal{G}^{\rm t}$
is non-void and compact; (b) every $\mu \in \mathcal{G}^{\rm t}$ obeys an
exponential integrability estimate, the same for the whole set
$\mathcal{G}^{\rm t}$; (c) every $\mu \in \mathcal{G}^{\rm t}$ has a
Lebowitz-Presutti type support; (d) $\mathcal{G}^{\rm t}$ is a singleton at
high temperatures. In the case of attractive interaction and $\nu=1$ we prove
that $|\mathcal{G}^{\rm t}|>1$ at low temperatures. The uniqueness of Gibbs
measures due to quantum effects and at a nonzero external field are also proven
in this case. Thereby, a qualitative theory of phase transitions and quantum
effects, which interprets most important experimental data known for the
corresponding physical objects, is developed. The mathematical result of the
paper is a complete description of the set $\mathcal{G}^{\rm t}$, which refines
and extends the results known for models of this type.
