2
$\begingroup$

In a numerical experiment, I have obtained a phase diagram of the system under study. The phase diagram is obtained between two scaled quantities say, $P^{\prime}$ and $Q^{\prime}$ of the system. I have seen that if the quantity $P$ is scaled by a factor say, $A=C\exp{(Q^{\prime})}$, where $C$ is a constant, I get the phase transition points ($P^{\prime}_{m}$ , $Q^{\prime}_{m}$), which follows the law :
$P^{\prime}_{m}=C_1\exp{(-Q^{\prime}_{m})}$, ( $C_1$ is a constant ),
which almost looks like $A=C\exp{(Q^{\prime})}$ (in the sense that both contains an exponential of $Q^{\prime}$) except the -ve sign infront of $Q^{\prime}_{m}$.

I am unable to figure out whether it carries some physical meaning or not. Is this a mere coincidence that the scale factor $A$ and scaled quantity $P^{\prime}_{m}$ depends similarly on scaled versions of $Q$, or, this does have a physical significance ?

$\endgroup$
2
  • $\begingroup$ "I have seen that if the quantity $P$ is scaled by a factor $A$..." should this be $P'$? If not what is the relationship between $P$ and $P'$? $\endgroup$ Commented Dec 20, 2022 at 18:29
  • $\begingroup$ The relation between $P$ and $P^{\prime}$ is : $P^{\prime}=\frac{P}{A}$ $\endgroup$
    – bubucodex
    Commented Dec 20, 2022 at 18:31

0