The temperature dependences of the dielectric properties at different fixed pressures, and the antiferroelectric phase transitions of squaric acid H2C4O4 and its deuterated form D2C4O4 have been investigated. Using the four-sublattice pseudospin cluster Hamiltonian, together with a pseudospin-phonon interaction term, the statistical Green’s-function technique has been applied to explain phenomenologically the isotope effect, dome-shaped temperature-dependent dielectric constant near the transition temperature Tc and the ‘‘crossover’’ behavior (first order to second order) in H2C4O4 crystals. The elongation of the O-H... O bonds alone, contrary to the implication of Samara and Semmingsen [J. Chem. Phys. 71, 1401 (1979)], is not sufficient to explain the isotope effect and other peculiar features of phase transitions in squaric acid. The model parameters, obtained by fitting the experimental electrical susceptibility data, have also been used to calculate heat capacity (C¯=A∂/∂T[Tχ(T)]) and reproduces a maximum value of C¯ at ≊7.0 K above Tc for the H2C4O4, which agrees with the corresponding experimental value. From our theoretical observation a unified character of the antiferroelectric transition in H2C4O4 and the antiferromagnetic transitions in some two-dimensional Ising systems is well exposed.