Abstract
With the use of the correlation function approach to multicomponent systems, the transition temperature is calculated within the mean-field approximation for a ternary alloy having arbitrary two-body and three-body interactions and arbitrary concentrations. This expression is studied in certain limiting cases. The concept of an effective concentration-dependent two-body interaction caused by the presence of three-body potentials is given justification. However, as has been pointed out for binary alloys and for mean-field approximations in general, this concept loses validity as the system approaches criticality and long-range correlations become dominant.