Landau scalar correlation length (source code)

= Landau scalar correlation length
{c}
{title2=$\xi=(r_0+u_0m_0^2/2)^{-1/2}$}

For a stable homogeneous scalar quartic saddle with <gradient> coefficient one, the <Ornstein--Zernike correlation function> has denominator $q^2+r_0+u_0m_0^2/2$. At zero source and $u_0>0$, the <correlation length> is $r_0^{-1/2}$ in the disordered phase and $(-2r_0)^{-1/2}$ on either selected ordered branch. Linear thermal tuning of $r_0$ gives <correlation-length critical exponent> $\nu=1/2$ with different amplitudes on the two sides.