The ordinary surface universality class of the three-dimensional O($N$) model

TL;DR

This paper investigates the critical behavior of the three-dimensional O(N) model at the surface universality class using high-precision Monte Carlo simulations, providing accurate estimates of surface critical exponents and fixed-point values.

Contribution

The study offers the first high-precision estimates of the surface field operator scaling dimension and fixed-point values for N=2,3,4 in the 3D O(N) model at the ordinary transition.

Findings

Precise surface field operator scaling dimensions for N=2,3,4.

Fixed-point values of RG-invariant observables at the ordinary transition.

Suppression of leading bulk scaling correction in the improved lattice model.

Abstract

We study the critical behavior at the ordinary surface universality class of the three-dimensional O($N$) 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.