Mean-field magnetic-susceptibility amplitude ratio (source code)

= Mean-field magnetic-susceptibility amplitude ratio
{title2=$\Gamma_+/\Gamma_-=2$}

For a scalar quartic <Landau free energy> with $a=a_0t$ and positive quartic coefficient, the zero-field susceptibility is $1/(a_0t)$ above the transition and $1/(2a_0|t|)$ within a selected ordered phase below it. Their singular amplitudes have ratio two. Below the transition this is a one-sided pure-phase response: the globally minimizing <magnetization> jumps between opposite phases when the field crosses zero. The mean-field ratio is not asserted to be exact in every fluctuation-dominated system.