  In Statistical Mechanics, Tsallis distributions were apparently conceived in
connection with systems presenting long--range interactions. In fact, they were
observed in numerical computations for models of such a type, as occurring in
the approach to equilibrium, i.e., to a Maxwell--Boltzmann distribution. Here
we exhibit two apparently new results. The first one is that Tsallis
distributions occur also in an ionic--crystal model with long--range Coulomb
forces, which is so realistic as to reproduce in an impressively good way the
experimental infrared spectra. Thus such distributions may be expected to be
actual physical features of crystals. The second result is that Tsallis
distributions occur in the standard short--range FPU model too, so that the
presence of long--range interactions is not a necessary condition for Tsallis
distributions to occur. In fact, this is in agreement with a previous result of
the first author in connection with the statistics of return times for the
classical FPU model. We thus confirm the thesis advanced by Tsallis himself,
that the relevant property for a dynamical system to present Tsallis
distributions is that its dynamics should be not fully chaotic, a property
which is known to actually pertain to long--range systems.
