Extraordinary-log Universality of Critical Phenomena in Plane Defects

TL;DR

This paper demonstrates the presence of extraordinary-log criticality in plane defects of 3D and 4D O(n) systems, providing numerical evidence and revealing new scaling relations, thereby advancing critical phenomena and conformal field theory.

Contribution

First numerical proof of E-Log criticality in 3D plane defects and discovery of its emergence in 4D, with insights into scaling relations for different n values.

Findings

E-Log criticality confirmed in 3D plane defects for n=2.

Scaling relation for n=2 matches theoretical predictions.

E-Log criticality also appears in 4D systems.

Abstract

The recent discovery of the extraordinary-log (E-Log) criticality is a celebrated achievement in modern critical theory and calls for generalization. Using large-scale Monte Carlo simulations, we study the critical phenomena of plane defects in three- and four-dimensional O($n$) critical systems. In three dimensions, we provide the first numerical proof for the E-Log criticality of plane defects. In particular, for $n=2$, the critical exponent $\hat{q}$ of two-point correlation and the renormalization-group parameter $\alpha$ of helicity modulus conform to the scaling relation $\hat{q}=(n-1)/(2 \pi \alpha)$, whereas the results for $n \geq 3$ violate this scaling relation. In four dimensions, it is strikingly found that the E-Log criticality also emerges in the plane defect. These findings have numerous potential realizations and would boost the ongoing advancement of conformal field theory.