  We consider tiles of some fixed size, with an associated weighting on the
shapes of tile, of total mass 1. We study the pressure, $p$, of tilings with
those tiles; the pressure, one over the volume times the logarithm of the
partition function. (The quantity we define as "pressure" could, perhaps
equally harmoniously with physics notation, be called "entropy per volume",
neither nomenclature is "correct".) We let $\hat p^0$ (easy to compute) be the
pressure in the limit of absolute smoothness (the weighting function is
constant). Then as smoothness, suitably defined, increases, $p$ converges to
$\hat p^0$, uniformly in the volume. It is the uniformity requirement that
makes the result non-trivial. This seems like a very basic result in the theory
of pressure of tilings. Though at the same time, perhaps non-glamorous, being
bereft of geometry and not very difficult. The problem arose for us out of
study of a problem in mathematical physics, associated to a model of
ferromagnetism.
