Spin correlations for the $\Lambda \Lambda$ and

$\Lambda \bar{\Lambda}$ pairs, generated in relativistic

heavy-ion collisions, and related angular correlations at the

joint registration of space-parity nonconserving hadronic decays

of two hyperons are theoretically analyzed. These correlations

give important information about the character and

mechanism of multiple processes, and the advantage of the

$\Lambda \Lambda$ and $\Lambda \bar{\Lambda}$ systems over

other ones is conditioned by the fact that the $P$-odd decays

$\Lambda \rightarrow p + \pi^-$ and

$\bar{\Lambda} \rightarrow \bar{p} + \pi^+$ serve as effective

analyzers of spin states of the $\Lambda$ and $\bar{\Lambda}$

particles -- thus, the respective spin correlations can be

rather easily distinguished and studied experimentally, which

is especially important for studies of multiple particle

generation at

modern and future ion colliders (RHIC, LHC, NICA).

The correlation

tensor components can be derived by the method of

"moments" -- as a result of averaging the combinations of

trigonometric functions of proton (antiproton) flight angles

over the double angular distribution of flight directions for

products of two decays. The properties of the "trace" $T$ of the

correlation tensor (a sum of three diagonal components),

which determines the angular correlations as well as the

relative fractions of the triplet states and singlet state of

respective pairs, are discussed.

In the present talk, spin correlations for two identical ($\Lambda

\Lambda$) and two non-identical ($\Lambda \bar{\Lambda}$) particles are generally considered from the viewpoint of the conventional model of one-particle sources. In the framework of this model, correlations vanish at enough large relative momenta. However, under these conditions (especially at

ultrarelativistic energies), in the case of two non-identical particles ($\Lambda \bar{\Lambda}$) the two-particle --

quark-antiquark and two-gluon -- annihilation sources start playing a noticeable role and lead to the difference of the

correlation tensor from zero. In particular, such a situation may arise, when the system passes through the "mixed phase" and -- due to the multiple production of free quarks and gluons in the process of deconfinement of hadronic matter -- the number

of two-particle sources strongly increases.