Two compounds of the 1-(4’-alkoxyphenylamino-3-[5’’-(2’’-menthylpirydil)]-propen-1-one-3 (PIRn) series that exhibit the hexatic-B (Hex-B) to smectic-A (Sm-A) and the crystal-B (Cry-B) to Hex-B phase transitions were studied by high resolution ac calorimetry. The Hex-B–Sm-A phase transition was found to be of first order and continuous for PIR7 and PIR9, respectively. The tricritical point was located at the concentration for which TCry−B–Hex−B/THex−B–Sm−A =0.980±0.004, i.e., a hexatic range of 7 K. At both sides of the tricritical point, nonclassical and non-three-dimensional-XY specific heat exponents α were observed. The Cry-B–Hex-B phase transition was of first order and was associated with a small or immeasurable Cp anomaly.