文摘
We study the four-dimensional n-component \({|\varphi|^4}\) spin model for all integers \({n \ge 1}\) and the four-dimensional continuous-time weakly self-avoiding walk which corresponds exactly to the case \({n=0}\) interpreted as a supersymmetric spin model. For these models, we analyse the correlation length of order p, and prove the existence of a logarithmic correction to mean-field scaling, with power \({\frac 12\frac{n+2}{n+8}}\), for all \({n \ge 0}\) and \({p > 0}\). The proof is based on an improvement of a rigorous renormalisation group method developed previously.