2016/02/12 by Roland Bauerschmidt, Bauerschmidt, Roland, David C. Brydges +3
Mathematics · Physics and Astronomy · #60K35 #82B27 #82B28 (Primary) #82B41 (Secondary) #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum many-body systems #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:60K35 #msc:82B27 #msc:82B28 #msc:82B41
paper · pdf · doi:10.48550/arxiv.1602.04048
Proceedings for ICMP, Santiago de Chile, July 2015
arxiv created 2016/02/12 · openalex publication_date 2016/02/12 · arxiv updated 2016/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an overview of results on critical phenomena in 4 dimensions, obtained recently using a rigorous renormalisation group method. In particular, for the n-component |φ|4 spin model in dimension 4, with small coupling constant, we prove that the susceptibility diverges with a logarithmic correction to the mean-field behaviour with exponent (n+2)/(n+8). This result extends rigorously to n=0, interpreted as a supersymmetric version of the model that represents exactly the continuous-time weakly self-avoiding walk. We also analyse the critical two-point function of the weakly self-avoiding walk, the specific heat and pressure of the |φ|4 model, as well as scaling limits of the spin field close to the critical point.