  Entanglement represents a pure quantum effect involving two or more
particles. Spin systems are good candidates for studying this effect and its
relation with other collective phenomena ruled by quantum mechanics. While the
presence of entangled states can be easily verified, the quantitative estimate
of this property is still under investigation. One of the most useful tool in
this framework is the concurrence whose definition, albeit limited to $S=1/2$
systems, can be related to the correlators. We consider quantum spin systems
defined along chains and square lattices, and described by Heisenberg-like
Hamiltonians: our goal is to clarify the relation between entanglement and
quantum phase transitions, as well as that between the concurrence the and the
specific quantum state of the system.
