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| -rw-r--r-- | ising_scaling.tex | 8 |
1 files changed, 8 insertions, 0 deletions
diff --git a/ising_scaling.tex b/ising_scaling.tex index 47b58ec..2301e73 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -487,6 +487,14 @@ For $\theta>\theta_c$, \end{equation} fixing $B$ and $F_c$. Since $A$ and $\tilde B$ are known exactly, these forms can be substituted. +This leaves as unknown variables the positions $\theta_0$ and +$\theta_{\mathrm{YL}}$ of the abrupt transition and Yang--Lee edge singularity, +the amplitude $A_\mathrm{YL}$ of the latter, and the unknown functions $F$ and +$h$. We determine these approximately by iteration in the polynomial order at +which the free energy and its derivative matches known results. Gradients can be computed with + +A Levenburg--Marquardt algorithm is performed + \begin{table} \begin{tabular}{c|ccc} $n$ & $\mathcal F_-^{(n)}$ & $\mathcal F_0^{(n)}$ & $\mathcal F_+^{(n)}$ \\\hline |