We study the critical behavior at the ordinary surface universality class of the three-dimensional $\mathrm{O}\left(N\right)$ model, bounded by a two-dimensional surface. Using high-precision Monte Carlo simulations of an improved lattice model, where the leading bulk scaling correction is suppressed, and finite-size scaling analysis of the fourth cumulant of the surface magnetization, we obtain precise estimates of the scaling dimension of the surface field operator for $N=2,3,4$. We also determine the fixed-point values of two renormalization-group invariant observables, which characterize the finite-size scaling behavior at the ordinary transition.

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• Conformal field theory
• Critical phenomena
• Surface & interfacial phenomena
• Classical spin models
• Finite-size scaling
• Monte Carlo methods
• O(N) symmetry