  We propose a new method of constructing the quantum Griffiths inequality.
From a viewpoint of operator inequalities, we first study the quantum rotor
model. This viewpoint clarifies important connections between the reflection
positivity and the Griffiths inequality. Next we apply our method to the
spin-$1/2$ quantum Heisenberg model. Finally we point out a model-independent
structure which governs the correlation inequalities.
