Operator multiplication is subtle in interacting theories compared to free theories. The operator product expansion of two operators with dimensions Δ Δ 1 and Δ Δ 2 will generally give not a unique operator but infinitely many operators, and their dimension will not generally be equal to Δ Δ 1 + Δ Δ 2 . In the above two-dimensional Ising model example, the operator product σ σ × × σ σ gives an operator ϵ ϵ whose dimension is 1 and not twice the dimension of σ σ .