  We investigate the low-energy properties as well as quantum and thermal phase
transitions of the Baxter-Wu model in a transverse magnetic field. Our study
relies on stochastic series expansion quantum Monte Carlo and on series
expansions about the low- and high-field limits at zero temperature using the
quantum finite-lattice method on the triangular lattice. The phase boundary
consists of a second-order critical line in the 4-state Potts model
universality class starting from the pure Baxter-Wu limit meeting a first-order
line connected to the zero-temperature transition point ($h\approx2.4$, $T=0$).
Both lines merge at a tricritical point approximatively located at ($h\approx
2.3J$, $T\approx J$).
