Boundary operator expansion and extraordinary phase transition in the tricritical O(N) model

TL;DR

This paper analyzes the boundary extraordinary transition in a 3D tricritical O(N) model, revealing an ordered boundary for any N and providing a novel example of continuous symmetry breaking in 2D boundary criticality.

Contribution

It computes the boundary operator expansion for the tricritical O(N) model using epsilon expansion, demonstrating an ordered boundary phase at the transition.

Findings

Boundary exhibits ordered phase for all N

First example of continuous symmetry breaking in 2D boundary criticality

Boundary operator expansion derived for transverse and longitudinal modes

Abstract

We study the boundary extraordinary transition of a three-dimensional (3D) tricritical $O(N)$ model. We first compute the mean-field Green's function with a general coupling of $|\vec \phi|^{2n}$ (with $n=3$ corresponding to the tricritical model) at the extraordinary phase transition. Then, using layer susceptibility, we obtain the boundary operator expansion for the transverse and longitudinal modes within the $\epsilon=3 - d$ expansion. Based on these results, we demonstrate that the tricritical point exhibits an extraordinary transition characterized by an ordered boundary for any $N$. This provides the first nontrivial example of continuous symmetry breaking in 2D in the context of boundary criticality.