Tensor network Monte Carlo study of the J1-J2 Ising model on the square lattice

Abstract

The frustrated square-lattice J1-J2 Ising model exhibits rich magnetic phases, yet its phase transitions remain difficult to characterize due to critical slowing down in conventional Monte Carlo and truncation errors inherent to tensor renormalization group methods. We develop a tensor-network Monte Carlo (TNMC) algorithm for this frustrated model, which supports both open and periodic boundary conditions. For periodic lattices, we use a sweeping block-update strategy that updates spin blocks while fixing surrounding spins. To boost efficiency, we couple our sampler with histogram reweighting, and test each technique standalone to validate these independent optimizations. We perform extensive finite-size scaling analyses at g=0.55 and g=1.0, extracting apparent critical temperatures and effective thermal exponents from Binder-cumulant data. Our method offers an efficient, nearly bias-free path for large-scale simulations of J1-J2-type frustrated magnets under periodic boundaries and generalizes readily to other frustrated spin lattices.

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BibTeX RIS

BibTeX

@misc{zheng2026tensor,
  title = {{Tensor network Monte Carlo study of the J1-J2 Ising model on the square lattice}},
  author = {Wanying Zheng and Tao Chen and Youjin Deng and Wanzhou Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25270},
  eprint = {2610.25270},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25270},
}

RIS

TY  - UNPB
TI  - Tensor network Monte Carlo study of the J1-J2 Ising model on the square lattice
AU  - Wanying Zheng
AU  - Tao Chen
AU  - Youjin Deng
AU  - Wanzhou Zhang
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.25270
UR  - https://arxiv.org/abs/2610.25270
AB  - The frustrated square-lattice J1-J2 Ising model exhibits rich magnetic phases, yet its phase transitions remain difficult to characterize due to critical slowing down in conventional Monte Carlo and truncation errors inherent to tensor renormalization group methods. We develop a tensor-network Monte Carlo (TNMC) algorithm for this frustrated model, which supports both open and periodic boundary conditions. For periodic lattices, we use a sweeping block-update strategy that updates spin blocks while fixing surrounding spins. To boost efficiency, we couple our sampler with histogram reweighting, and test each technique standalone to validate these independent optimizations. We perform extensive finite-size scaling analyses at g=0.55 and g=1.0, extracting apparent critical temperatures and effective thermal exponents from Binder-cumulant data. Our method offers an efficient, nearly bias-free path for large-scale simulations of J1-J2-type frustrated magnets under periodic boundaries and generalizes readily to other frustrated spin lattices.
ER  -

Abstract

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