A Renormalisation Group Map for Short- and Long-ranged Weakly Coupled $|Ï|^4$ Models in $d \ge 4$ at and Above the Critical Point

Jiwoon Park

paper

A Renormalisation Group Map for Short- and Long-ranged Weakly Coupled $∣ I ¨ ∣^{4}$ Models in $d \geq 4$ at and Above the Critical Point

arXiv:2511.03495

Abstract

In this article, we construct and analyse a renormalisation group (RG) map for the weakly coupled $n$ -component $∣ I ¨ ∣^{4}$ model under periodic boundary conditions in dimension $d \geq 4$ . Both short-range and long-range interactions with upper critical dimension four are considered. This extends and refines the RG map constructed by Bauerschmidt, Brydges and Slade for the short-range model at $d = 4$ . This extension opens the door to establishing the exact decay rate of correlation functions of all of the models discussed. Furthermore, incorporating a large-field decay estimate and comparing with the finite-size scaling results of Michta, Park, and Slade, our analysis provides strong evidence for the emergence of a plateau in systems of finite volume with periodic boundary conditions.

94 pages

A Renormalisation Group Map for Short- and Long-ranged Weakly Coupled ∣I¨∣4 Models in d≥4 at and Above the Critical Point

Abstract

A Renormalisation Group Map for Short- and Long-ranged Weakly Coupled $∣ I ¨ ∣^{4}$ Models in $d \geq 4$ at and Above the Critical Point