  We prove polynomial decay of the mixing field of the Vertex Reinforced Jump
Process (VRJP) on $\Bbb{Z}^2$ with bounded conductances. Using [17] we deduce
that the VRJP on $\Bbb{Z}^2$ with any constant conductances is almost surely
recurrent. It gives a counterpart of the result of Merkl, Rolles [14] and
Sabot, Zeng [17] for the 2-dimensional Edge Reinforced Random Walk.
