The heat capacity of a Cs2ZnI4 single crystal has been measured by mea
ns of AC calorimetry. Three anomalies have been detected corresponding
to a normal to inconmensurate phase transition at T-I = 116.9+/-0.1 K
, an incommensurate to commensurate lock-in transition at T-L = 107.58
+/-0.05 K, and a structural transition from a commensurate orthorhombi
c to a monoclinic phase at T-C = 93.77+/-0.05 K with thermal hysteresi
s. The lock-in transition has the peculiarity of being discontinuous b
ut not showing any measurable hysteresis. After comparison with the La
ndau model predictions for the heat capacity, derived for the k(Delta)
= (1/2 + Delta)a case, it is concluded that Cs2ZnI4 lies close to th
e Lifschitz point of coexistence of the normal, incommensurate and com
mensurate phases.