We extend a previously developed technique for computing spin-spin critical correlators in the 2d Ising model, to the case of multiple correlations. This enables us to derive Kadanoff-Ceva's formula in a simple and elegant way. We also exploit a doubling procedure in order to evaluate the critical exponent of the polarization operator in the Baxter model. Thus we provide a rigorous proof of the relation between different exponents, in the path-integral framework.