  We show that the vertex-reinforced jump process on the d-dimensional lattice
with long-range jumps is transient as long as the initial weights do not decay
too fast. The main ingredients in the proof are: the relation of the
corresponding random environment on finite boxes with a non-linear
supersymmetric hyperbolic sigma model, a comparison with a hierarchical model,
and the translation of the hierarchical model to a non-homogeneous effective
one-dimensional model.
