Extraordinary-log Universality of Critical Phenomena in Plane Defects

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.