We study the four-dimensional n-component | φ| 4 spin model for all integers n≥ 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 12n+2n+8, for all n≥ 0 and p> 0. The proof is based on an improvement of a rigorous renormalisation group method developed previously.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics