= Mean-field scalar free-energy scaling
{title2=$A_s=a|t|^2f_\pm(bh/|t|^{3/2})$}
For a scalar quartic <Landau free energy> $r_tt m^2/2+um^4/4-hm$ with $r_t,u>0$, rescaling $m=(r_t/u)^{1/2}|t|^{1/2}\psi$ gives this minimized scaling form, with $a=r_t^2/u$ and $b=\sqrt u/r_t^{3/2}$. The two functions minimize $\pm\psi^2/2+\psi^4/4-H\psi$. In particular $f_+(0)=0$ and $f_-(0)=-1/4$. Below the transition the equilibrium field dependence has a cusp at zero; pure-phase derivatives are one-sided. The form gives <order-parameter critical exponent> $\beta=1/2$ and <magnetic-susceptibility critical exponent> $\gamma=1$.
Back to article page
