  We present the phase diagram and critical properties of a coupled $XY$-Ising
model on a triangular lattice using the mean-field approximation, the
Migdal-Kadanoff scheme of renormalization group and Monte-Carlo simulations.
The topology of the phase diagram is similar for the three techniques, with the
appearance of a phase with $XY$ order and Ising disorder. The results suggest a
line of transitions belonging to the 2D-Ising universality class in contrast
with previous data indicating a new universality class. This model is relevant
to the columnar phases of discotic liquid crystals [such as
hexa(hexylthio)triphenylene (HHTT)] in the limit of weak intercolumn coupling.
