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