parameter, $\psi_0$, related to the composition and three non–conserved order parameter components $(\psi_1, \psi_2, \psi_3)$. These are defined by the following equations:

$$\begin{aligned}
\psi_0 = m_1 + m_2 + m_3 + m_4, \nonumber \\
\psi_1 = m_1 - m_2 - m_3 + m_4, \nonumber \\
\psi_2 = m_1 - m_2 + m_3 - m_4,  \\
\psi_3 = m_1 + m_2 - m_3 - m_4,  \nonumber\end{aligned}$$

where $m_{\alpha}$ are the differences of the mean $A$– and $B$–occupation numbers, $m_\alpha = \langle{c^A_i}\rangle - \langle{c^B_i}\rangle$ for $i \in \alpha$. The index $\alpha = 1\dots4$ enumerates the four equivalent simple–cubic sublattices of the fcc–structure. For a homogeneous $A_3B$ alloy, $\psi_0 = 2$. In the disordered phase, $\psi_1=\psi_2=\psi_3=0$, while the four equivalent ordered phases are described as $(\psi_1,
\psi_2,\psi_3)/\bar \psi$ = $(-1,1,1)$; $(1,-1,1)$; $(1,1,-1)$ and $(-1,-1,-1)$, with a temperature–dependent $\bar \psi$ ($\bar \psi = 2$ at $T=0$). For a non–homogeneous system Eq. (2) gives the corresponding local order parameters for each (cubic) elementary fcc–cell in terms of weighted averages of the occupation numbers computed of all sites belonging to the cell. (The weights are taken as the inverse of the numbers of neighboring fcc–cells that “share” the site in question, i. e. functions 1/2 and 