  We introduce the concepts of geometric classical and total correlations
through Schatten 1-norm (trace norm), which is the only Schatten p-norm able to
ensure a well-defined geometric measure of correlations. In particular, we
derive the analytical expressions for the case of two-qubit Bell-diagonal
states, discussing the superadditivity of geometric correlations. As an
illustration, we compare our results with the entropic correlations, discussing
both their hierarchy and monotonicity properties. Moreover, we apply the
geometric correlations to investigate the ground state of spin chains in the
thermodynamic limit. In contrast to the entropic quantifiers, we show that the
classical correlation is the only source of 1-norm geometric correlation that
is able to signaling an infinite-order quantum phase transition.
