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1 files changed, 23 insertions, 15 deletions
diff --git a/ising_scaling.tex b/ising_scaling.tex index ca1bd15..d4ea507 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -582,22 +582,30 @@ accuracy of the fit results can be checked against the known values here. \begin{table}\label{tab:fits} \begin{tabular}{c|lll} $m$ & \multicolumn{1}{c}{$\mathcal F_-^{(m)}$} & $\mathcal F_0^{(m)}$ & $\mathcal F_+^{(m)}$ \\\hline - 0 & \hphantom{$-$}0 & $-1.197\,733\,383\,797\ldots$ & \hphantom{$-$}0 \\ - 1 & $-1.357\,838\,341\,707\ldots$ & \hphantom{$-$}$0.318\,810\,124\,891\ldots$ & \hphantom{$-$}0 \\ - 2 & $-0.048\,953\,289\,720\ldots$ & \hphantom{$-$}$0.110\,886\,196\,683(2)$ & $-1.845\,228\,078\,233\ldots$ \\ - 3 & \hphantom{$-$}$0.038\,863\,932(3)$ & $-0.016\,426\,894\,65(2)$ & \hphantom{$-$}0 \\ - 4 & $-0.068\,362\,119(2)$ & $-2.639\,978(1)\times10^{-4}$ & \hphantom{$-$}$8.333\,711\,750(5)$ \\ - 5 & \hphantom{$-$}$0.183\,883\,70(1)$ & \hphantom{$-$}$5.140\,526(1)\times10^{-4}$ & \hphantom{$-$}0 \\ - 6 & $-0.659\,171\,4(1)$ & \hphantom{$-$}$2.088\,65(1)\times 10^{-4}$ & $-95.168\,96(1)$ \\ - 7 & \hphantom{$-$}$2.937\,665(3)$ & \hphantom{$-$}$4.481\,9(1)\times10^{-5}$ & \hphantom{$-$}0 \\ - 8 & $-15.61(1)$ & \hphantom{$-$}$3.16\times10^{-7}$ & \hphantom{$-$}1457.62(3) \\ - 9 & \hphantom{$-$}96.76 & $-4.31\times10^{-6}$ & \hphantom{$-$}0 \\ - 10 & $-679$ & $-1.99\times10^{-6}$ & $-25\,891(2)$ \\ - 11 & \hphantom{$-$}$5.34\times10^3$ & & \hphantom{$-$}0 \\ - 12 & $-4.66\times10^4$ & & \hphantom{$-$}$5.02\times10^5$ \\ - 13 & \hphantom{$-$}$4.46\times10^5$ & & \hphantom{$-$}0 \\ - 14 & $-4.66\times10^6$ & & $-1.04\times10^7$ + 0 & \hphantom{$-$}0 & $-1.197\,733\,383\,797\ldots$ & \hphantom{$-$}0 \\ + 1 & $-1.357\,838\,341\,707\ldots$ & \hphantom{$-$}$0.318\,810\,124\,891\ldots$ & \hphantom{$-$}0 \\ + 2 & $-0.048\,953\,289\,720\ldots$ & \hphantom{$-$}$0.110\,886\,196\,683(2)$ & $-1.845\,228\,078\,233\ldots$ \\ + 3 & \hphantom{$-$}$0.038\,863\,932(3)$ & $-0.016\,426\,894\,65(2)$ & \hphantom{$-$}0 \\ + 4 & $-0.068\,362\,119(2)$ & $-2.639\,978(1)\times10^{-4}$ & \hphantom{$-$}$8.333\,711\,750(5)$ \\ + 5 & \hphantom{$-$}$0.183\,883\,70(1)$ & \hphantom{$-$}$5.140\,526(1)\times10^{-4}$ & \hphantom{$-$}0 \\ + 6 & $-0.659\,171\,4(1)$ & \hphantom{$-$}$2.088\,65(1)\times 10^{-4}$ & $-95.168\,96(1)$ \\ + 7 & \hphantom{$-$}$2.937\,665(3)$ & \hphantom{$-$}$4.481\,9(1)\times10^{-5}$ & \hphantom{$-$}0 \\ + 8 & $-15.61(1)$ & \hphantom{$-$}$3.16\times10^{-7}$ & \hphantom{$-$}1457.62(3) \\ + 9 & \hphantom{$-$}96.76 & $-4.31\times10^{-6}$ & \hphantom{$-$}0 \\ + 10 & $-679$ & $-1.99\times10^{-6}$ & $-25\,891(2)$ \\ + 11 & \hphantom{$-$}$5.34\times10^3$ & & \hphantom{$-$}0 \\ + 12 & $-4.66\times10^4$ & & \hphantom{$-$}$5.02\times10^5$ \\ + 13 & \hphantom{$-$}$4.46\times10^5$ & & \hphantom{$-$}0 \\ + 14 & $-4.66\times10^6$ & & $-1.04\times10^7$ \end{tabular} + \caption{ + Known series coefficients for the universal scaling functions. This with + trailing dots are known exactly or have closed integral representations. + Those with listed uncertainties are taken from Mangazeev \textit{et al.}\ + \cite{Mangazeev_2008_Variational}. Those without are taken from Fonseca + \textit{et al.}, and are assumed to be accurate to within their last digit + \cite{Fonseca_2003_Ising}. + } \end{table} \begin{table} |