Renormalisation group analysis of weakly self-avoiding walk in dimensions four and higher

TL;DR

This paper rigorously proves that the critical two-point function for weakly self-avoiding walk decays as |x|^{-(d-2)} in four and higher dimensions using a renormalisation group approach.

Contribution

It provides a rigorous renormalisation group proof of the decay behavior of the critical two-point function in four and higher dimensions.

Findings

Critical two-point function decays as |x|^{-(d-2)} in d=4 and higher.

The proof uses a rigorous renormalisation group method.

Validates theoretical predictions for self-avoiding walks in high dimensions.

Abstract

We outline a proof, by a rigorous renormalisation group method, that the critical two-point function for continuous-time weakly self-avoiding walk on Z^d decays as |x|^{-(d-2)} in the critical dimension d=4, and also for all d>4.