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arXiv · 1511.02790

Finite-order correlation length for 4-dimensional weakly self-avoiding walk and $|\varphi|^4$ spins

Roland Bauerschmidt·Gordon Slade·Alexandre Tomberg·Benjamin C. Wallace
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Abstract

We study the 4-dimensional $n$-component $|\varphi|^4$ spin model for all integers $n \ge 1$, and the 4-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.

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Roland Bauerschmidt, Gordon Slade, Alexandre Tomberg, Benjamin C. Wallace. 2015-11-09. Finite-order correlation length for 4-dimensional weakly self-avoiding walk and $|\varphi|^4$ spins. https://doi.org/10.1007/s00023-016-0499-0

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