Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary

Abstract

It was recently realized that the three-dimensional O($N$) model possesses an extraordinary boundary universality class for a finite range of $N\ge 2$. For a given $N$, the existence and universal properties of this class are predicted to be controlled by certain amplitudes of the normal universality class, where one applies an explicit symmetry breaking field to the boundary. In this Letter, we study the normal universality class for $N=2,3$ using Monte Carlo simulations on an improved lattice model and extract these universal amplitudes. Our results are in good agreement with direct Monte Carlo studies of the extraordinary universality class serving as a nontrivial quantitative check of the connection between the normal and extraordinary classes.

arXiv comment16 pages, 2 figures, including Supplemental Material; v2: expanded discussion, 19 pages, 2 figures, including Supplemental Material

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• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Symmetry protected topological phases under decoherence
• Notes on a Surface Defect in the $O(N)$ Model
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