  We study effects of perturbation Hamiltonian to quantum spin systems which
can include quenched disorder. Model-independent inequalities are derived,
using an additional artificial disordered perturbation. These inequalities
enable us to prove that the variance of the perturbation Hamiltonian density
vanishes in the infinite volume limit even if the artificial perturbation is
switched off. This theorem is applied to spontaneous symmetry breaking
phenomena in a disordered classical spin model, a quantum spin model without
disorder and a disordered quantum spin model.
