On this example, the objective is to obtain ⟨ ⟨ M ⟩ ⟩ and ⟨ ⟨ M 2 ⟩ ⟩ (for instance, to obtain the magnetic susceptibility of the system) since it is straightforward to generalize to other observables. According to the definition, M ( r → → ) = ∑ ∑ i = 1 N σ σ i .