Monte Carlo simulations based on effective interactions obtained from
first-principles calculations reveal the existence of three ordered ph
ases in ternary Cu2NiZn: (i) ''modified''-L1(0) (0-600 K), (ii) L1(2)
(600-850 K), and (iii) L1(0) (850-1200 K). This is in contrast to the
generally accepted picture which assumes the existence of only two. We
demonstrate that this sequence of phases is a consequence of the symm
etry of the ground state and the magnitude of the dominating pair inte
ractions. It agrees with available experimental data.