Bilayer XY Model

This Monte Carlo simulation program contains two implementations for studying bilayer XY models with different coupling mechanisms. These models are important for understanding phase transitions in layered spin systems.

The first implementation simulates the two-body coupling bilayer XY model with Hamiltonian:

where $\ell = a, b$ represents layer a and layer b. We set temperature as 1 and tune the parameters $J$ and $K$ to explore the phase diagram.

The second implementation focuses on four-body interactions between layers, with Hamiltonian:

Note: These are the names from the original version of the model — “two body” corresponds to “single” in the latest version, and “four body” corresponds to “pair.”

How to use

1. Clone the repository:

   git clone https://github.com/Tensofermi/Bilayer_XY_Model
   cd Bilayer_XY_Model

2. Configure model selection in Makefile:

   SRC_DIR := src_2_body
   # SRC_DIR := src_4_body

   Uncomment the desired model and comment the other.

3. Set parameters in input.txt and run the simulation:

   ./run.sh
   

4. For advanced simulations, including job submissions on HPC systems, refer to the /lsub, /qsub and /data directories in our related project: Zoo_of_Classical_ON_Spin_Model.

Physics Results

Our simulations measure single-layer correlations and paired correlations to distinguish different phases in these models:

Two-Body Model

• Two distinct phases identified: disorder phase and BKT phase
• Critical exponent $\eta$ at BKT transition points matches theoretical predictions
• Strong agreement between numerical and analytical results

Four-Body Model

• Three-phase structure discovered: disorder phase, paired BKT phase, and conventional BKT phase
• Novel paired BKT phase exists as an intermediate state between disordered and conventional BKT phases
• Non-trivial behavior observed at phase boundaries

These findings are thoroughly documented in our paper: arXiv:2504.01461 or Phys. Rev. B 112, 144420(2025).

Citation

If you use this code or refer to our results in your research, please cite:

@article{xiao2025fate,
  title={Fate of Berezinskii-Kosterlitz-Thouless Paired Phase in Coupled $ XY $ Models},
  author={Xiao, Tianning and Deng, Youjin and Dong, Xiao-Yu},
  journal={arXiv preprint arXiv:2504.01461},
  year={2025}
}

or

@article{1hkf-t4wy,
  title = {Fate of the Berezinskii-Kosterlitz-Thouless paired phase in coupled $XY$ models},
  author = {Xiao, Tianning and Deng, Youjin and Dong, Xiao-Yu},
  journal = {Phys. Rev. B},
  volume = {112},
  issue = {14},
  pages = {144420},
  numpages = {15},
  year = {2025},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/1hkf-t4wy},
  url = {https://link.aps.org/doi/10.1103/1hkf-t4wy}
}