Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional $O(N)$ model

Abstract

Recent advances in boundary critical phenomena have led to the discovery of a new surface universality class in the three-dimensional $O(N)$ model. The newly found ``extraordinary-log" phase can be realized on a two-dimensional surface for $N<N_c$, with $N_c>3$, and on a plane defect embedded into a three-dimensional system, for any $N$. One of the key features of the extraordinary-log phase is the presence of logarithmic violations of standard finite-size scaling. In this work we study finite-size scaling in the extraordinary-log universality class by means of Monte Carlo simulations of an improved lattice model. We simulate the model with open boundary conditions, realizing the extraordinary-log phase on the surface for $N=2,3$, as well as with fully periodic boundary conditions and in the presence of a plane defect for $N=2,3,4$. In line with theory predictions, renormalization-group invariant observables studied here exhibit a logarithmic dependence on the size of the system. We numerically access not only the leading term in the $\beta$-function governing these logarithmic violations, but also the subleading term, which controls the evolution of the boundary phase diagram as a function of $N$.

18 pages, 11 figures; v2: 21 pages, 11 figures, expanded sec. III.D, results unchanged

References in corpus (19)

• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Quantum criticality under decoherence or weak measurement
• Intrinsically Gapless Topological Phases
• Measurements conspire nonlocally to restructure critical quantum states
• Unconventional Surface Critical Behaviors Induced by Quantum Phase Transition from Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to Néel Order
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Extraordinary-log surface phase transition in the three-dimensional $XY$ model
• A plane defect in the 3d O$(N)$ model
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• Three-dimensional $O(N)$-invariant ${\varphi }^4$ models at criticality for $N\ge 4$
• Extraordinary-log Universality of Critical Phenomena in Plane Defects
• Bulk and Surface Critical Behaviors of quantum Heisenberg antiferromagnet on a two-dimensional coupled diagonal ladders
• The ordinary surface universality class of the three-dimensional O($N$) model
• Finite-Size Scaling at fixed Renormalization-Group invariant

Cited by in corpus (3)

• Topological physics in quantum critical systems
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class