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diff --git a/ising_scaling.tex b/ising_scaling.tex index 3f11729..919049e 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -332,6 +332,40 @@ the low-temperature zero-field (phase coexistence) line. In practice the infinite series in \eqref{eq:schofield.funcs} cannot be entirely fixed, and it will be truncated at finite order. +\begin{figure} + \begin{gnuplot}[terminal=epslatex] + t0 = 1.36261 + g0 = 0.438453 + g1 = -0.0531270 + g2 = -0.00391478 + g3 = -0.000408016 + g4 = 0.0000262629 + g5 = -0.00000109745 + + g(t) = (1-(t/t0)**2)*(g0*t + g1*t**3 + g2*t**5 + g3*t**7 + g4*t**9 + g5*t**11) + + set xlabel '$u_t$' + set ylabel '$u_h$' + set key left bottom reverse title '\raisebox{1em}{$R$}' + + set xzeroaxis + set yzeroaxis + + set parametric + set trange [-t0:t0] + + plot \ + (1-t**2),g(t) title '$1$', \ + 2*(1-t**2),2*g(t) title '$2$', \ + 4*(1-t**2),4*g(t) title '$4$' + \end{gnuplot} + \caption{ + Example of the parametric coordinates. Lines are of constant $R$ from + $-\theta_0$ to $\theta_0$ for $g(\theta)$ taken from the $n=6$ entry of + Table \ref{tab:fits}. + } \label{fig:schofield} +\end{figure} + One can now see the convenience of these coordinates. Both invariant scaling combinations depend only on $\theta$, as \begin{align} |