Isobaric Critical Exponents: Test of Analyticity Against NIST Reference Data - Cho, Wonyoung; Kim, Do-Hyun; Park, Jeong-Hyuck (Frontiers in Physics, 2018)
Finite systems may undergo first or second order phase transitions under not isovolumetric but isobaric condition. The `analyticity' of a finite-system partition function has been argued to imply universal values for isobaric critical exponents, $α_{{\scriptscriptstyle{P}}}$, $β_{{\scriptscriptstyle{P}}}$ and $γ_{{\scriptscriptstyle{P}}}$. Here we test this prediction by analyzing NIST REFPROP data for twenty major molecules, including $\mathrm{H_{2}O, CO_{2}, O_{2}}$, etc. We report they are consistent with the prediction for temperature range, $10^{-5} <|T/T_{c}-1|<10^{-3}$. For each molecule, there appears to exist a characteristic natural number, $n=2,3,4,5,6$, which determines all the critical exponents for $T<T_{c}$ as $α_{{\scriptscriptstyle{P}}}=γ_{{\scriptscriptstyle{P}}}=\frac{n}{n+1}$ and $β_{{\scriptscriptstyle{P}}}=δ^{-1}=\frac{1}{n+1}$. For the opposite $T>T_{c}$, all the fluids seem to indicate the universal value of ${n=2}$.