  Critical phenomena theory centers on the scaled thermodynamic potential per
spin $\phi(\beta, h)=|t|^{p}Y(h|t|^{-q})$, with inverse temperature
$\beta=1/T$, $h=-\beta H$, ordering field $H$, reduced temperature
$t=t(\beta)$, critical exponents $p$ and $q$, and function $Y(z)$ of
$z=h|t|^{-q}$. I discuss calculating $Y(z)$ with the information geometry of
thermodynamics. Scaled solutions obtain with three admissible functions
$t(\beta)$: 1) $t=e^{-J\beta}$, 2) $t=\beta^{-1}$, and 3) $t=\beta_C-\beta$,
where $J$ and $\beta_C$ are constants. For $p=q$, information geometry yields
$Y(z)=\sqrt{1+z^2}$, consistent with the one-dimensional (1D) ferromagnetic
Ising model.
