  We investigate a witness for nonclassical multipartite states based on their
disturbance under local measurements. The witness operator provides a
sufficient condition for nonclassicality that coincides with a nonvanishing
global quantum discord, but it does not demand an extremization procedure.
Moreover, for the case of Z_2-symmetric systems, we rewrite the witness in
terms of correlation functions so that classicality is found to necessarily
require either vanishing magnetization in the invariant axis or isotropy of the
two-point function in the transverse spin plane. We illustrate our results in
quantum spin chains, where a characterization of factorized ground states (with
spontaneously broken Z_2 symmetry) is achieved. As a by-product, the witness
will also be shown to indicate a second-order quantum phase transitions, which
will be illustrated both for the XY and Ashkin-Teller spin chains.
