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We present the phase diagram and critical properties of a coupled $XY$-Isingmodel on a triangular lattice using the mean-field approximation, theMigdal-Kadanoff scheme of renormalization group and Monte-Carlo simulations.The topology of the phase diagram is similar for the three techniques, with theappearance of a phase with $XY$ order and Ising disorder. The results suggest aline of transitions belonging to the 2D-Ising universality class in contrastwith previous data indicating a new universality class. This model is relevantto the columnar phases of discotic liquid crystals [such ashexa(hexylthio)triphenylene (HHTT)] in the limit of weak intercolumn coupling.Comment: 11 figures available upon reques

Thermal phase diagram of a model Hamiltonian for columnar phases of liquid crystals