  We address the one-dimensional quantum Ising model as an example of system
exhibiting criticality and study in some details the discrimination problem for
pairs of states corresponding to different values of the coupling constant. We
evaluate the error probability for single-copy discrimination, the Chernoff
bound for $n$-copy discrimination in the asymptotic limit, and the Chernoff
metric for the discrimination of infinitesimally close states. We point out
scaling properties of the above quantities, and derive the external field
optimizing state discrimination for short chains as well as in the
thermodynamical limit, thus assessing criticality as a resource for quantum
discrimination in many-body systems.
