Persistence of BKT phase transition in the 2D nonanalytic XY model

@misc{hu2026persistence,
  title = {{Persistence of BKT phase transition in the 2D nonanalytic XY model}},
  author = {Sihan Hu and Xianzhi Pan and Kun Chen and Yi Jiang and Youjin Deng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12560},
  eprint = {2609.12560},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12560},
}

TY  - UNPB
TI  - Persistence of BKT phase transition in the 2D nonanalytic XY model
AU  - Sihan Hu
AU  - Xianzhi Pan
AU  - Kun Chen
AU  - Yi Jiang
AU  - Youjin Deng
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12560
UR  - https://arxiv.org/abs/2609.12560
AB  - We study the two-dimensional XY model with the nonanalytic pair potential 2[(1−cosδ)/2]^p, whose small-angle law ∝|δ|^2p carries a cusp for p<1 and a flat bottom for p>1, invalidating the harmonic spin-wave expansion. Two questions arise: the nature of the low-temperature (T) phase and of the phase transition. A naive energetic argument would predict genuine long-range order and an enhanced transition temperature for p<1, and no transition at all for p>1. Large-scale Monte Carlo simulations contradict both: for every p>0 the \dengrevxxi{low-T phase} is quasi-long-range ordered, with anomalous dimension η(T)∝ T^1/p, and terminates at a Berezinskii--Kosterlitz--Thouless transition. Using a vortex-free noncompact lattice-field description and utilizing a duality transformation, we show that coarse-graining drives the height-difference distribution onto a single Gaussian fixed point, renormalizing the cusp and flatness into a finite harmonic stiffness that restores the spin-wave description and the BKT scenario for all p>0.
ER  -