  We study and compare the persistence of bipartite entanglement (BE) and
multipartite entanglement (ME) in one-dimensional and two-dimensional spin XY
models in an external transverse magnetic field under the effect of thermal
excitations. We compare the threshold temperature at which the entanglement
vanishes in both types of entanglement. We use the entanglement of formation as
a measure of the BE and the geometric measure to evaluate the ME of the system.
We have found that in both dimensions in the anisotropic and partially
anisotropic spin systems at zero temperatures, all types of entanglement decay
as the magnetic field increases but are sustained with very small magnitudes at
high field values. Also we found that for the same systems, the threshold
temperatures of the nearest neighbour (nn) BEs are higher than both of the
next-to-nearest neighbour BEs and MEs and the three of them increase
monotonically with the magnetic field strength. Thus, as the temperature
increases, the ME and the far parts BE of the system become more fragile to
thermal excitations compared to the nn BE. For the isotropic system, all types
of entanglement and threshold temperatures vanish at the same exact small value
of the magnetic field. We emphasise the major role played by both the
properties of the ground state of the system and the energy gap in controlling
the characteristics of the entanglement and threshold temperatures. In
addition, we have shown how an inserted magnetic impurity can be used to
preserve all types of entanglement and enhance their threshold temperatures.
Furthermore, we found that the quantum effects in the spin systems can be
maintained at high temperatures, as the different types of entanglements in the
spin lattices are sustained at high temperatures by applying sufficiently high
magnetic fields.
