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

TL;DR

This paper investigates the boundary critical behavior of the 3D O(N) model, focusing on the transition from normal to extraordinary universality classes, using Monte Carlo simulations to verify theoretical predictions.

Contribution

It provides the first quantitative Monte Carlo analysis of the normal universality class for N=2,3, confirming the predicted connection to the extraordinary class.

Findings

Universal amplitudes for N=2,3 extracted from simulations.

Good agreement with theoretical predictions.

Validation of the boundary universality class connection.

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.