A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems - II. Critical behavior of susceptibility and correlation length

Continuing the analysis started in Part I of this work, we investigate critical phenomena in weakly coupled φ{symbol}⁴ spin systems in four dimensions. Concerning the critical behavior of the susceptibility and the correlation length (in the high-temperature phase), the existence of logarithmic corrections to their mean field type behavior is rigorously shown (i.e., we prove χ(t)~t^{- 1} |ln t|^1/3, ξ(t)~t^-1/2|ln t}|^1/6).