Spell check and added a reference.

1 files changed, 6 insertions, 4 deletions

diff --git a/ising_scaling.tex b/ising_scaling.tex
index 8488f9d..2b1fb62 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -171,7 +171,7 @@ use $\xi=u_h|u_t|^{-\Delta}$ and $\eta=u_t|u_h|^{-1/\Delta}$.
 The analyticity of the free energy at places away from the critical point
 implies that the functions $\mathcal F_\pm$ and $\mathcal F_0$ have power-law
 expansions of their arguments about zero, the result of so-called Griffiths
-analyticity. For instance, when $u_t$ goes to zero for nonzero $u_h$ there is
+analyticity \cite{Griffiths_1967_Thermodynamic}. For instance, when $u_t$ goes to zero for nonzero $u_h$ there is
 no phase transition, and the free energy must be an analytic function of its
 arguments. It follows that $\mathcal F_0$ is analytic about zero. This is not
 the case at infinity: since
@@ -896,7 +896,7 @@ values of both are plotted.
     Free parameters in the fit of the parametric coordinate transformation and
     scaling form to known values of the scaling function series coefficients
     for $\mathcal F_\pm$. The fit at stage $n$ matches those coefficients up to
-    and including order $n$. Error estimates are difficult to quantify directly.
+    and including order $n$. Uncertainty estimates are difficult to quantify directly.
   } \label{tab:fits}
 \end{table}
 
@@ -1013,7 +1013,7 @@ Fig.~\ref{fig:phi.series}.
     The series coefficients for the scaling function $\mathcal F_-$ as a
     function of polynomial order $m$. The numeric values are from Table
     \ref{tab:data}, and those of Caselle \textit{et al.} are from the most
-    accurate scaling function listed in \cite{Caselle_2001_The}. The deviation at high polynomial order illustrates the lack of the essential singularity in Caselle's form.
+    accurate scaling function listed in \cite{Caselle_2001_The}. The deviation at high polynomial order illustrates the lack of the essential singularity in the form of Caselle \textit{et al.}.
   } \label{fig:glow.series}
 \end{figure}
 
@@ -1186,7 +1186,9 @@ the ratio.
     Sequential ratios of the series coefficients of the scaling function
     $\mathcal F_-$ as a function of inverse polynomial order $m$. The
     extrapolated $y$-intercept of this plot gives the radius of convergence of
-    the series, which should be zero due to the essential singularity (as seen in the known numeric values and in this work). Cassel {\em et al} do not incorporate the essential singularity.
+    the series, which should be zero due to the essential singularity (as seen
+    in the known numeric values and in this work). Caselle \textit{et al.} do
+    not incorporate the essential singularity.
   } \label{fig:glow.radius}
 \end{figure}