  We study the robustness of multipartite entanglement of the ground state of
the one-dimensional spin 1/2 XY model with a transverse magnetic field in the
presence of thermal excitations, by investigating a threshold temperature,
below which the thermal state is guaranteed to be entangled. We obtain the
threshold temperature based on the geometric measure of entanglement of the
ground state. The threshold temperature reflects three characteristic lines in
the phase diagram of the correlation function. Our approach reveals a region
where multipartite entanglement at zero temperature is high but is thermally
fragile, and another region where multipartite entanglement at zero temperature
is low but is thermally robust.
