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arXiv · 2501.06287

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

Xinyu Sun·Shao-Kai Jian
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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 $|\vec ϕ|^{2n}$ (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 $ε=3 - d$ 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.

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Xinyu Sun, Shao-Kai Jian. 2025-05-22. Boundary operator expansion and extraordinary phase transition in the tricritical O(N) model. https://doi.org/10.21468/scipostphys.18.6.210

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