  We propose a gravity dual of antiferromagnetic quantum phase transition (QPT)
induced by magnetic field and study the critical behavior around the quantum
critical point (QCP). It turns out that the boundary critical theory is a
strong coupling theory with dynamic exponent $z=2$ and that the hyperscaling
law is violated and logarithmic corrections appear near the QCP. Some novel
scaling relations are predicated, which can be tested by experiment data in
future. We also make some comparison with experimental data on low-dimensional
magnets BiCoPO$_5$ and pyrochlores Er$_{2-2x}$Y$_{2x}$Ti$_2$O$_7$.
