Boundary critical behavior of the three-dimensional Heisenberg universality class

Abstract

We study the boundary critical behavior of the three-dimensional Heisenberg universality class, in the presence of a bidimensional surface. By means of high-precision Monte Carlo simulations of an improved lattice model, where leading bulk scaling corrections are suppressed, we prove the existence of a special phase transition, with unusual exponents, and of an extraordinary phase with logarithmically decaying correlations. These findings contrast with naïve arguments on the bulk-surface phase diagram, and allow us to explain some recent puzzling results on the boundary critical behavior of quantum spin models.

11 pages, 3 figures, including Supplemental Material; v2: expanded discussion and technical details, results unchanged, 12 pages, 3 figures including Supplemental Material; v3: incorporates erratum, correct fit of helicity modulus, other results unchanged, 12 pages, 3 figures

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Cited by in corpus (36)

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• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Critical Casimir Effect: Exact Results
• Extraordinary-log surface phase transition in the three-dimensional $XY$ model
• A plane defect in the 3d O$(N)$ model
• Magnetic impurities at quantum critical points: large-$N$ expansion and SPT connections
• Surface criticality of antiferromagnetic Potts model
• Extraordinary-log Universality of Critical Phenomena in Plane Defects
• Surface critical properties of the three-dimensional clock model
• Special Transition and Extraordinary Phase on the Surface of a Two-Dimensional Quantum Heisenberg Antiferromagnet
• Analytic bootstrap for magnetic impurities
• Quantum extraordinary-log universality of boundary critical behavior
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Bulk and Surface Critical Behaviors of quantum Heisenberg antiferromagnet on a two-dimensional coupled diagonal ladders
• Sublattice extraordinary-log phase and new special point of the antiferromagnetic Potts model
• The ordinary surface universality class of the three-dimensional O($N$) model
• Measuring the Boundary Gapless State and Criticality via Disorder Operator
• Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model
• Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional $O(N)$ model
• Topological physics in quantum critical systems
• Extraordinary surface critical behavior induced by symmetry-protected topological state of a two-dimensional quantum magnet
• Boundary operator expansion and extraordinary phase transition in the tricritical O(N) model
• Finite-Size Scaling at fixed Renormalization-Group invariant
• Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model
• Boundary criticality for the Gross-Neveu-Yukawa models
• Boundary phase transitions of two-dimensional quantum critical XXZ model
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Deep Boundary Perturbations at a Quantum Critical Point
• Surface critical behavior of the three-dimensional O(3) model
• Deconfined Quantum Critical Point with Non-locality
• Boundary critical behavior of the Gross-Neveu-Yukawa model
• Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter