A Plane Defect in the 3D O(N) Model

It was recently found that the classical 3d O(N) model in the semi-infinite geometry supports an "extraordinary-log" boundary universality class, where the spin-spin correlation function on the boundary for spins separated by distance x falls off as (log x)^-q. This universality class exists for a range 2 ≤ N < N_c; Monte-Carlo simulations indicate N_c > 3. In this work, we extend this analysis to the 3d O(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 ≥ 2. We additionally show that the line of defect fixed points which is present at N = ∞ is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N corrections in agreement with our RG analysis. Furthermore, at N = ∞ we show that the defect ``central charge" a = 0 is constant along the line of fixed points, in agreement with a theorem of Jensen and O'Bannon. Finally, we revisit the problem of the O(N) model in the semi-infinite geometry. We find evidence that at N = N_c the extraordinary and special fixed points annihilate and only the ordinary fixed point is left for N > N_c.