  We report on high-resolution specific-heat and magnetocaloric-effect
measurements of the triangular-lattice antiferromagnets CsMn(Br_xI_{1-x})_3
with different x. The evolution of the magnetic phase diagrams from the
easy-axis system for x = 0 to the easy-plane system for x = 1 was studied in
detail. The specific-heat critical exponent alpha of the almost isotropic x =
0.19 system agrees with the value predicted for a chiral Heisenberg scenario.
In an applied magnetic field (B = 6 T) a crossover to a weak first-order
transition is detected.
