We analyse the perturbative renormalisation group flow derived in the previous chapter. When nonperturbative effects are ignored, we show how this analysis leads to a logarithmic correction to mean-field scaling for the 4-dimensional hierarchical susceptibility. Nonperturbative effects however cannot be ignored, and we state the extension of the results for the perturbative flow to its nonperturbative version and use this extension to prove the main results for the |φ|4 model. The analysis of the nonperturbative effects is carried out in subsequent chapters. The notion of infrared asymptotic freedom is discussed.