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-rw-r--r--ising_scaling.bib16
-rw-r--r--ising_scaling.tex10
2 files changed, 22 insertions, 4 deletions
diff --git a/ising_scaling.bib b/ising_scaling.bib
index 0d0dc51..11ae107 100644
--- a/ising_scaling.bib
+++ b/ising_scaling.bib
@@ -377,3 +377,19 @@
doi = {10.1007/bf01210832}
}
+info: 'Griffiths_1967' has been autocompleted into 'Griffiths_1967_Thermodynamic'.
+@article{Griffiths_1967_Thermodynamic,
+ author = {Griffiths, Robert B.},
+ title = {Thermodynamic Functions for Fluids and Ferromagnets near the Critical Point},
+ journal = {Physical Review},
+ publisher = {American Physical Society (APS)},
+ year = {1967},
+ month = {6},
+ number = {1},
+ volume = {158},
+ pages = {176--187},
+ url = {https://doi.org/10.1103%2Fphysrev.158.176},
+ doi = {10.1103/physrev.158.176}
+}
+
+
diff --git a/ising_scaling.tex b/ising_scaling.tex
index 00de5e3..7fa1ae6 100644
--- a/ising_scaling.tex
+++ b/ising_scaling.tex
@@ -182,7 +182,7 @@ 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
@@ -909,7 +909,7 @@ 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}
@@ -1026,7 +1026,7 @@ 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}
@@ -1199,7 +1199,9 @@ 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}