Reflection positivity and quantum Griffiths' inequalities

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.