Nematic order in monomer-dimer models of Heilmann and Lieb with lateral attraction in dimensions $d\ge 2$

We study the $d$-dimensional generalization of Models II ($d=2$) and V ($d=3$) for liquid crystals introduced by Heilmann--Lieb (1979), which consists of dimers on the hypercubic lattice at chemical potential $μ$, interacting via a hard-core repulsion and a lateral attraction between parallel dimers