High-dimensional Ising model

This Monte Carlo simulation program is designed to simulate the Ising model in its loop representation.

The partition function of the loop representation on a lattice graph $G$ can be written as

where $V$ is the number of vertices, $|G|$ is the total number of lattice bonds, and $G_b$ is a subset of the lattice graph $G$. The notation $G_b \in \mathrm{even}$ denotes the summation over even graphs, and $|G_b|$ represents the number of bonds in the graph $G_b$. The parameter $K = \beta J$ is the coupling strength of the Ising model.

The update scheme is based on the lifting technique; see the paper: Phys. Rev. E 97, 042126

Note that the complete version of the code is located in old_version/, which is written in Fortran. For convenience, the C++ version in src/ only implements the configuration update function.

How to use

1. Clone the repository:

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

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

   ./run.sh
   

3. 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.

Citation

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

@article{PhysRevE.109.034125,
  title = {Finite-size scaling of the high-dimensional Ising model in the loop representation},
  author = {Xiao, Tianning and Li, Zhiyi and Zhou, Zongzheng and Fang, Sheng and Deng, Youjin},
  journal = {Phys. Rev. E},
  volume = {109},
  issue = {3},
  pages = {034125},
  numpages = {10},
  year = {2024},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevE.109.034125},
  url = {https://link.aps.org/doi/10.1103/PhysRevE.109.034125}
}