Nuclear liquid-gas phase transitions are investigated in the framework of static antisymmetrized molecular dynamics (static AMD) model under either a constant volume or a constant pressure. A deuteron quadrupole momentum fluctuation thermometer is applied to extract the temperature of fragmenting systems of $^{36}$Ar and $^{100}$Sn. A plateau structure of caloric curves is observed under a constant volume for those system with a density $rho leq$ 0.03 fm$^{-3}$. A clear backbending in the caloric curves, which indicates a first order phase transition, is observed under a constant pressure with all pressures studied. The similar behavior of caloric curves of $^{36}$Ar and $^{100}$Sn systems indicates that there is no strong system size effect under a constant volume or a constant pressure. Both the mass distributions and the light particle multiplicities show a strong $alpha$ clusterization at low excitation energies in the static AMD simulations. The liquid-gas phase transition measures of the multiplicity derivative (dM/dT) and the normalized variance of $Z_{max}$ (NVZ) are applied. The experimental caloric curves are also compared with those of $^{100}$Sn of the static AMD simulations under both the constant volume and the constant pressure conditions. Discussions are presented with the available experimental results and those from the static AMD simulations. Large errors in the experimental temperature measurements and those in the reconstruction technique for the primary fragmenting source hinder to draw a conclusion whether the phase transition occurs under either a constant volume or a constant pressure. This study suggests that different measures for the liquid-gas phase transitions should be examined besides the caloric curves in order to draw a conclusion.
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