  Luttinger liquid (LL) phase refers to a quantum phase which emerges in the
ground state phase diagram of quite often low-dimensional quantum magnets as
spin-1/2 XX, XYY and frustrated chains. It is believed that the quasi
long-range order exists between particles forming the system in the LL phase.
Here, at the first step we concentrate on the study of correlated spin
particles in the one-dimensional (1D) spin-1/2 XX model which is exactly
solvable. We show that the spin-1/2 particles form string orders with an even
number of spins in the LL phase of the 1D spin-1/2 XX model. As soon as the
transverse magnetic field is applied to the system, string orders with an odd
number of spins induce in the LL phase. All ordered strings of spin-1/2
particles will be destroyed at the quantum critical transverse field, $h_c$. No
strings exist in the saturated ferromagnetic phase. At the second step we focus
on the LL phase in the ground state phase diagram of the 1D spin-1/2 XYY and
frustrated ferromagnetic models. We show that the even-string orders exist in
the LL phase of the 1D spin-1/2 XYY model but in the LL phase of the 1D
spin-1/2 frustrated ferromagnetic model we found all kind of strings. In
addition, the existence of a clear relation between the long-distance
entanglement and string orders in the LL phase is shown. Also, the effect of
the thermal fluctuations on the behavior of the string orders is studied.
