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arXiv · 1602.04048

Renormalisation group analysis of 4D spin models and self-avoiding walk

Roland Bauerschmidt·David C. Brydges·Gordon Slade
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Abstract

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 $|\varphi|^4$ 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 $|\varphi|^4$ model, as well as scaling limits of the spin field close to the critical point.

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Roland Bauerschmidt, David C. Brydges, Gordon Slade. 2016-02-12. Renormalisation group analysis of 4D spin models and self-avoiding walk. https://arxiv.org/abs/1602.04048

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