  The Bozonisation identities of [Dub11] show that squared 2d-Ising order and
disorder correlations are equal to +- the ratio of bipartite dimer partition
functions. In this self-contained paper, we give another proof of these
identities using the approach of [BdT14]. Our proof is more direct and allows
to keep track of order and disorder in XOR-Ising configurations.
