  This paper is the second in a series of papers considering symmetry
properties of a bosonic quantum system over an 2D graph, with continuous spins,
in the spirit of the Mermin--Wagner theorem. Here we consider bosonic systems
on bi-dimensional graphs where particles can jump from a vertex to another (a
generalized Hubbard model). The Feynman--Kac representation is used for proving
that if the local Hamiltonians are invariant under a continuous group of
transformations ${\tt G}$ (a Euclidean space or a torus of dimension $d'$
acting on a torus of dimension $d\geq d'$) then any infinite-volume Gibbs state
from a certain class (introduced in the paper) is also ${\tt G}$-invariant.
