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Diffstat (limited to 'ising_scaling.tex')
| -rw-r--r-- | ising_scaling.tex | 49 |
1 files changed, 28 insertions, 21 deletions
diff --git a/ising_scaling.tex b/ising_scaling.tex index bfa67fb..161a4e6 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -480,15 +480,16 @@ analytic for all $\theta\in\mathbb C$ outside the Langer branch cuts. The scaling function has a number of free parameters: the position $\theta_c$ of the abrupt transition, prefactors in front of singular functions from the abrupt transition and the Yang--Lee point, the coefficients in the analytic part of $\mathcal F$, and the coefficients in the undetermined function $h$. \begin{table} - \begin{tabular}{c|ccccccccc} + \begin{tabular}{c|cccccccccc} & \multicolumn{9}{c}{$n$} \\ - & 1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 & 17 \\ + & 0 & 1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 & 17 \\ \hline\hline - $n_-$ & 2 & 3 & 3 & 4 & 5 & 6 & 6 & 6 \\ - $n_0$ & 1 & 2 & 3 & 4 & 4 & 5 & 7 & 8 \\ - $n_+$ & 2 & 2 & 4 & 4 & 6 & 6 & 6 & 8 + $n_-$ & 2 & 2 & 3 & 3 & 4 & 5 & 6 & 6 & 6 \\ + $n_0$ & 0 & 1 & 2 & 3 & 4 & 4 & 5 & 7 & 8 \\ + $n_+$ & 2 & 2 & 2 & 4 & 4 & 6 & 6 & 6 & 8 \\ \hline $\theta_c$ & + 1.19426 & 1.19022 & 1.24954 & 1.24954 & @@ -499,6 +500,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of 1.33347 & \\ $A_c$ & + 0.0982351 & 0.100228 & 0.0720104 & 0.0809725 & @@ -509,6 +511,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of 0.0328499 & \\ $A_{\mathrm{YL}}$ & + 2.38365 & 2.3876 & 2.37518 & 2.46094 & @@ -519,6 +522,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of 2.4769 & \\ $F_0$ & + 1.07666 & 1.07383 & 1.14375 & 1.16003 & @@ -529,6 +533,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of 1.33327 & \\ $F_1$ & + 2.00381 & 1.99663 & 2.14753 & 2.15397 & @@ -539,6 +544,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of 2.50906 & \\ $F_2$ & + 0.228234 & 0.228235 & 0.226794 & 0.240421 & @@ -549,6 +555,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of 0.232317 & \\ $h_0$ & + 1.19426 & 1.19078 & 1.2259 & 1.18183 & @@ -558,7 +565,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of 1.21605 & 1.21825 & \\ - $h_1/10^{-2}$ & + $h_1/10^{-2}$ & & $0.0377284$ & $-1.32208$ & $-1.98552$ & @@ -568,7 +575,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of $-5.53426$ & $-5.79592$ & \\ - $h_2/10^{-3}$ & + $h_2/10^{-3}$ & & & 1.68015 & 3.72445 & @@ -578,7 +585,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of 9.31123 & 9.7244 & \\ - $h_3/10^{-3}$ & & + $h_3/10^{-3}$ & & & $-0.300336$ & $-1.11915$ & $-1.68817$ & @@ -587,7 +594,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of $-2.6766$ & $-2.79303$ & \\ - $h_4/10^{-4}$ & & & + $h_4/10^{-4}$ & & & & $2.59026$ & $4.92004$ & $6.6988$ & @@ -595,7 +602,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of $8.83288$ & $9.25784$ & \\ - $h_5/10^{-4}$ & & & + $h_5/10^{-4}$ & & & & $-0.578821$ & $-1.50074$ & $-2.55766$ & @@ -603,54 +610,54 @@ The scaling function has a number of free parameters: the position $\theta_c$ of $-3.30063$ & $-3.4621$ & \\ - $h_6/10^{-4}$ & & & & + $h_6/10^{-4}$ & & & & & $0.350651$ & $0.965437$ & $1.24302$ & $1.29961$ & $1.36707$ & \\ - $h_7/10^{-5}$ & & & & + $h_7/10^{-5}$ & & & & & $-0.617004$ & $-3.5398$ & $-5.06226$ & $-5.40426$ & $-5.70884$ & \\ - $h_8/10^{-5}$ & & & & & + $h_8/10^{-5}$ & & & & & & $0.978241$ & $1.90968$ & $2.22565$ & $2.40644$ & \\ - $h_9/10^{-6}$ & & & & & + $h_9/10^{-6}$ & & & & & & $-1.76567$ & $-6.25434$ & $-8.84571$ & $-10.1167$ & \\ - $h_{10}/10^{-6}$ & & & & & & + $h_{10}/10^{-6}$ & & & & & & & $1.51279$ & $3.12976$ & $4.0249$ & \\ - $h_{11}/10^{-7}$ & & & & & & + $h_{11}/10^{-7}$ & & & & & & & $-2.17053$ & $-9.37655$ & $-14.7593$ & \\ - $h_{12}/10^{-7}$ & & & & & & & + $h_{12}/10^{-7}$ & & & & & & & & $2.0809$ & $4.687$ & \\ - $h_{13}/10^{-8}$ & & & & & & & + $h_{13}/10^{-8}$ & & & & & & & & $-2.83978$ & $-12.363$ & \\ - $h_{14}/10^{-8}$ & & & & & & & & + $h_{14}/10^{-8}$ & & & & & & & & & $2.39528$ & \\ - $h_{15}/10^{-9}$ & & & & & & & & + $h_{15}/10^{-9}$ & & & & & & & & & $-2.99667$ & \\ \end{tabular} @@ -718,7 +725,7 @@ The scaling function has a number of free parameters: the position $\theta_c$ of set xlabel '$1/n$' set xrange [0:0.55] set ylabel '$\mathcal F_n/\mathcal F_{n-1}$' - set yrange [0:10] + set yrange [0:15] plot \ dat1 using (1/$1):(abs(ratLast($2))) title 'Numeric', \ |