  We study an M-p-spin spin glass model with p=3 and M=3 in three dimensions
using the Migdal-Kadanoff renormalization group approximation (MKA). In this
version of the p-spin model, there are three (M=3) Ising spins on each site. At
mean-field level, this model is known to have two transitions; a dynamical
transition and a thermodynamic one at a lower temperature. The dynamical
transition is similar to the mode-coupling transition in glasses, while the
thermodynamic transition possibly describes what happens at the Kauzmann
temperature. We find that all the coupling constants in the model flow under
the MKA to the high-temperature sink implying that the mean-field features
disappear in three dimensions and that there is no transition in this model.
The behavior of the coupling constant flow is qualitatively similar to that of
the model with p=3 and M=2, for which only a single transition is predicted at
the mean-field level. We conclude that for p-spin models in three dimensions,
fluctuation effects completely remove all traces of their mean-field behavior.
