A plane defect in the 3d O(N) model

Abstract

It was recently found that the classical 3d O(N)(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as \langle \vec{S}(x) \cdot \vec{S}(0)\rangle \sim \frac{1}{(\log x)^q}〈S→(x)⋅S→(0)⟩∼1(logx)q. This universality class exists for a range 2 ≤N <N_c2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate N_c > 3Nc>3. In this work, we extend this result to the 3d O(N)(N) model in an infinite geometry with a plane defect. We use renormalization group (RG) to show that in this case the extraordinary-log universality class is present for any finite N ≥2N≥2. We additionally show, in agreement with our RG analysis, that the line of defect fixed points which is present at N = ∞N=∞ is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N1/N corrections. We study the “central charge” aa for the O(N)O(N) model in the boundary and interface geometries and provide a non-trivial detailed check of an aa-theorem by Jensen and O’Bannon. Finally, we revisit the problem of the O(N)(N) model in the semi-infinite geometry. We find evidence that at N = N_cN=Nc the extraordinary and special fixed points annihilate and only the ordinary fixed point is left for N > N_cN>Nc.