AUTHOR=Cho Wonyoung , Kim Do-Hyun , Park Jeong-Hyuck 

TITLE=Isobaric Critical Exponents: Test of Analyticity Against NIST Reference Data

JOURNAL=Frontiers in Physics

VOLUME=Volume 6 - 2018

YEAR=2018

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2018.00112

DOI=10.3389/fphy.2018.00112

ISSN=2296-424X

ABSTRACT=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, $\alpha_{{\scriptscriptstyle{P}}}$, $\beta_{{\scriptscriptstyle{P}}}$ and $\gamma_{{\scriptscriptstyle{P}}}$. 
Here we test this prediction   by analyzing   NIST REFPROP data  for twenty major molecules, including $\mathrm{H_{2}O, CO_{2}, O_{2}}$,  \textit{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 $\alpha_{{\scriptscriptstyle{P}}}=\gamma_{{\scriptscriptstyle{P}}}=\frac{n}{n+1}$ and $\beta_{{\scriptscriptstyle{P}}}=\delta^{-1}=\frac{1}{n+1}$.  For the opposite $T>T_{c}$,   all the fluids  seem to indicate   the universal value of ${n=2}$.