Extraordinary-log Universality of Critical Phenomena in Plane Defects
Yanan Sun, Minghui Hu, Youjin Deng, Jian-Ping Lv
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 $\mathrm{O}(n)$ 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 $\stackrel{^}{q}$ of two-point correlation and the renormalization-group parameter $\ensuremath{\alpha}$ of helicity modulus conform to the scaling relation $\stackrel{^}{q}=(n\ensuremath{-}1)/(2\ensuremath{\pi}\ensuremath{\alpha})$, whereas the results for $n\ensuremath{\ge}3$ 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.