  We study the ground state quantum correlation of Ising model in a transverse
field (ITF) by implementing the quantum renormalization group (QRG) theory. It
is shown that various quantum correlation measures and the
Clauser-Horne-Shimony-Holt inequality will highlight the critical point related
with quantum phase transitions, and demonstrate nonanalytic phenomena and
scaling behavior when the size of the systems becomes large. Our results also
indicate a universal behavior of the critical exponent of ITF under QRG theory
that the critical exponent of different measures is identical, even when the
quantities vary from entanglement measures to quantum correlation measures.
This means that the two kinds of quantum correlation criterion including the
entanglement-separability paradigm and the information-theoretic paradigm have
some connections between them. These remarkable behaviors may have important
implications on condensed matter physics because the critical exponent directly
associates with the correlation length exponent.
