Abstract
The combinatorial Bosonisation identities of [5] show that the square of 2d-Ising order and disorder correlations are equal to ± the ratio of bipartite dimer partition functions. In this self-contained paper, we give an alternative proof of these identities using the approach of [2]. Our proof is more direct and allows to see the eect of order and disorder on XOR-Ising polygon congurations.