  We use a mixed-spin model, with aperiodic ferromagnetic exchange interactions
and crystalline fields, to investigate the effects of deterministic geometric
fluctuations on first-order transitions and tricritical phenomena. The
interactions and the crystal field parameters are distributed according to some
two-letter substitution rules. From a Migdal-Kadanoff real-space
renormalization-group calculation, which turns out to be exact on a suitable
hierarchical lattice, we show that the effects of aperiodicity are
qualitatively similar for tricritical and simple critical behaviour. In
particular, the fixed point associated with tricritical behaviour becomes fully
unstable beyond a certain threshold dimension (which depends on the
aperiodicity), and is replaced by a two-cycle that controls a weakened and
temperature-depressed tricritical singularity.
