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Weakly self-avoiding walk in dimension four

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We report on recent and ongoing work on the continuous-time weakly self-avoiding walk on the 4-dimensional integer lattice, with focus on a proof that the susceptibility diverges at the critical point with a logarithmic correction to mean-field scaling. The method of proof, which is of independent interest, is based on a rigorous renormalisation group analysis of a supersymmetric field theory representation of the weakly self-avoiding walk. The talk is based on collaborations with David Brydges, and with Roland Bauerschmidt and David Brydges.

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