We study the nearest-neighbour Ising and φ^4 models on \mathbb Z^d with d≥3 and obtain new lower bounds on their two-point functions at (and near) criticality. Together with the classical infrared bound, these bounds turn into up-to constant estimates when d≥5. When d=4, we obtain an ''almost'' sharp lower bound corrected by a logarithmic factor. As a consequence of these results, we show that η=0 and ν=1/2 when d≥4, where η is the critical exponent associated with the decay of the model's two-point function at criticality and ν is the critical exponent of the correlation length ξ(β). When d=3, we improve previous results and obtain that η≤1/2. As a byproduct of our proofs, we also derive the blow-up at criticality of the so-called bubble diagram when d=3,4.
