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

Abstract

It was recently found that the classical 3d O(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 S(x) • S(0) ∼ 1 (log x) q . This universality class exists for a range 2 ≤ N < N c and Monte-Carlo simulations and conformal bootstrap indicate N c > 3. In this work, we extend this result 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, in agreement with our RG analysis, 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. We study the "central charge" a for the O(N ) model in the boundary and interface geometries and provide a non-trivial detailed check of an a-theorem by 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 .

Boundaries and interfaces with localized cubic interactions in the O(N) model

“…Using a combination of Renormalization Group (RG) analysis and 1/N expansion, they demonstrated the existence of the 3D "extraordinary log" universality class. For boundaries, this class exists only for N smaller than a critical value which is above 3 [20][21][22], but for the interfaces it appears to exist for all N [23].…”

“…While the extraordinary universality class for boundaries or interfaces was known to exist in bulk dimension greater than 3, it was not completely clear what happens to it for D = 3. During JHEP10(2023)017 the past three years, this problem was revisited in papers [20][21][22][23]. Using a combination of Renormalization Group (RG) analysis and 1/N expansion, they demonstrated the existence of the 3D "extraordinary log" universality class.…”