Lattice energy-momentum tensor with Symanzik improved actions

We define the energy-momentum tensor on a lattice for the {λ}φ⁴ and for the nonlinear {σ}-model Symanzik tree-improved actions, using Ward identities or an explicit matching procedure. The resulting operators give the correct one loop scale anomaly, and in the case of the {σ} model they can have applications in Monte Carlo simulations.