as the finite difference on neighboring lattice locations i , j . Then δ δ h [ u ^ ^ ] → → ∂ ∂ μ μ u ^ ^ in the limit h → → 0 , and u ^ ^ i ⋅ ⋅ u ^ ^ j → → ∂ ∂ μ μ u ^ ^ ⋅ ⋅ ∂ ∂ μ μ u ^ ^ after dropping the constant terms u ^ ^ i ⋅ ⋅ u ^ ^ i = 1 (the "bulk magnetization").