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diff --git a/ising_scaling.tex b/ising_scaling.tex index 744f2d5..0bf301e 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -691,95 +691,87 @@ to their known values at the critical isotherm, or $\theta=1$. \begin{tabular}{|c|lllllll} \hline \multicolumn{1}{|c|}{$n$} & + \multicolumn{1}{c}{$\theta_0$} & \multicolumn{1}{c}{$\theta_\mathrm{YL}$} & \multicolumn{1}{c}{$C_\mathrm{YL}$} & \multicolumn{1}{c}{$G_1$} & \multicolumn{1}{c}{$G_2$} & \multicolumn{1}{c}{$G_3$} & - \multicolumn{1}{c}{$G_4$} & - \multicolumn{1}{c}{$G_5$} \\ + \multicolumn{1}{c}{$G_4$} \\ \hline 2 & - 0.198152 & - 2.39338 & - 1.52182 & - 0.455868 \\ + 1.14841 & + 0.989667 & + $-0.172824$ & + $-0.310183$ & + 0.247454 \\ 3 & - 0.199048 & - 2.25700 & - 1.30767 & - 0.396157 \\ + 1.25421 & + 0.602056 & + $-0.385664$ & + $-0.352751$ & + 0.258243 \\ 4 & - 0.198918 & - 2.36150 & - 1.46058 & - 0.307198 & - \hphantom{$-$}0.0323334 \\ + 1.31649 & + 0.640019 & + $-0.356397$ & + $-0.355055$ & + 0.234659 & + $-0.00190837$ \\ 5 & - 0.198100 & - 2.43224 & - 1.55298 & - 0.362791 & - $-0.108393$ & - 0.0228573 \\ + 1.34032 & + 0.623811 & + $-0.380029$ & + $-0.351275$ & + 0.237046 & + $-0.00731973$ \\ 6 & - 0.197027 & - 2.45864 & - 1.59639 & - 0.484865 & - $-0.119149$ & - 0.0150607 \\ - 7 & - 0.196809 & - 2.49636 & - 1.65176 & - 0.54349 & - $-0.141089$ & - 0.00877823 & - $-0.00110698$ \\ - \hline - \end{tabular} - \begin{tabular}{|c|llllll} - \hline - $n$ & - \multicolumn{1}{c}{$\theta_0$} & - \multicolumn{1}{c}{$g_1$} & - \multicolumn{1}{c}{$g_2$} & - \multicolumn{1}{c}{$g_3$} & - \multicolumn{1}{c}{$g_4$} & - \multicolumn{1}{c}{$g_5$} \\ - \hline - 2 & - 1.22182 & - $-0.0140696$ \\ - 3 & - 1.33128 & - $-0.0144135$ & - $-0.000233014$ \\ - 4 & - 1.33106 & - $-0.0268822$ & - \hphantom{$-$}$0.0332121$ \\ - 5 & - 1.51661 & - $-0.248646$ & - \hphantom{$-$}$0.0513219$ & - $0.00433870$ \\ - 6 & - 1.37654 & - $-0.236244$ & - $-0.00860939$ & - 0.00204312 & - $-0.000954046$ \\ - 7 & - 1.33161 & - $-0.252714$ & - $-0.0308462$ & - 0.00491578 & - \hphantom{$-$}0.000264989 & - $-0.000210698$ \\ + 1.36261 & + 0.646215 & + $-0.355764$ & + $-0.352058$ & + 0.233166 & + $-0.00664903$ & + $-0.00168991$ \\ \hline \end{tabular} + \begin{tabular}{|c|llllll} + \hline + $n$ & + \multicolumn{1}{c}{$g_0$} & + \multicolumn{1}{c}{$g_1$} & + \multicolumn{1}{c}{$g_2$} & + \multicolumn{1}{c}{$g_3$} & + \multicolumn{1}{c}{$g_4$} & + \multicolumn{1}{c}{$g_5$} \\ + \hline + 2 & + 0.373691 & + $-0.0216363$ \\ + 3 & + 0.448379 & + $-0.0220323$ & + \hphantom{$-$}0.000222006 \\ + 4 & + 0.441074 & + $-0.0348177$ & + \hphantom{$-$}0.000678173 & + $-0.0000430514$ \\ + 5 & + 0.443719 & + $-0.0460994$ & + $-0.000745834$ & + \hphantom{$-$}0.0000596688 & + $-0.00000440308$ \\ + 6 & + 0.438453 & + $-0.0531270$ & + $-0.00391478$ & + $-0.000408016$ & + \hphantom{$-$}0.0000262629 & + $-0.00000109745$ \\ + \hline + \end{tabular} \caption{ Free parameters in the fit of the parametric coordinate transformation and scaling form to known values of the scaling function series coefficients |