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In earlier work we showed that in the bulk, the correlation of gaps in dimersystems on the hexagonal lattice is governed, in the fine mesh limit, byCoulomb's law for 2D electrostatics. We also proved that the scaling limit ofthe discrete field ${\bold F}$ of average tile orientations is, up to amultiplicative constant, the electric field produced by a 2D system of chargescorresponding to the gaps. In this paper we show that in the bulk, the relativechange $T_{\al,\be}$ in correlation caused by displacing a hole by a fixedvector $(\al,\be)$ is, in the fine mesh limit, the projection on $(\al,\be)$ ofa new field ${\bold T}$, which is also equal up to a multiplicative constant tothe electric field of the corresponding system of charges. We also discuss thedifferences between the fields ${\bold T}$ and ${\bold F}$ and presentconjectures for their fine mesh limits in the more general case of a dimersystem with boundary. The new field ${\bold T}$ can be viewed as capturing theinstantaneous pull on each gap in the surrounding fluctuating sea of dimers.From the point of view of the parallel to physics, the electrostatic forceemerges then as an entropic force.

The effect of microscopic gap displacement on the correlation of gaps in dimer systems