Spontaneous Magnetization

Spontaneous magnetization $m$ in an Ising ferromagnet appears below the critical temperature $T_c$. The derivative of $m$ diverges in the limit $T \to T_c^-$.

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% Spontaneous magnetization m in an Ising ferromagnet appears below the critical temperature T_c.
% The derivative of m diverges in the limit $T \to T_c^-$.
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}[
    declare function={
        % arcsinh
        arcsinh(\x) = ln(\x + sqrt(\x^2+1));
        % magnetization
        m(\x) = and(\x>=0,\x<1) * (1 - (sinh(arcsinh(1)/x))^(-4))^(1/8) + or(\x<0,\x>=1) * (0);
      }]
  \begin{axis}[
      xlabel = {$T/T_c$},
      ylabel = {$m(0,T)$},
      smooth,thick,
      domain=0:1.8,
      ymax=1.6,
      axis lines = center,
      every tick/.style = {thick}]
    \addplot[color=blue,very thick,samples=300]{m(x)};
    \addplot[color=black,dashed,domain=0:1]{x};
  \end{axis}
\end{tikzpicture}
\end{document}
 
 
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