Bilayer Coulomb phase of two-dimensional dimer models: Absence of power-law columnar order

Using renormalization group (RG) analyses and Monte Carlo (MC) simulations, we study the fully packed dimer model on the bilayer square lattice with fugacity equal to z (1) for interlayer (intralayer) dimers, and intralayer interaction V between neighboring parallel dimers on any elementary plaquette in either layer. For a range of not-too-large z>0 and repulsive interactions 00 destroys the power-law correlations of the z=0 decoupled layers, and leads immediately to a short-range correlated state, albeit with a slow crossover for small |V|. For V_{c}