Phase transitions of the antiferromagnetic J1-J2-J3 Ising model on the cubic lattice
Abstract
Motivated by the conflicting findings in prior studies regarding the nature of the phase transition for the three-dimensional antiferromagnetic J1-J2-J3 Ising model on the cubic lattice with J1 = J2 = J3 = 1.0, in this study we conduct a detailed investigation of this model using both Monte Carlo simulations and neural networks (NN). Here J1 and J2 are the intralayer nearest-neighbor and next-nearest-neighbor couplings, respectively, and J3 is the nearest-neighbor interlayer interaction. By investigating the data obtained from much larger lattices than those used in previous studies, we find that the phase transition for J1 = J2 = J3 = 1.0 is second order without any ambiguity. Hence we bring a resolution to this debate. Apart from J1 = J2 = J3 = 1.0, we study the critical phenomenon associated with J2/J1 = 4/7 and J3 = J1 = 1.0 as well. In addition, by employing a dedicated training and testing strategy, our NN computation not only is much more efficient than those utilizing the standard procedures commonly used in the literature, but also requires only a per-mille fraction of the storage capacity needed by a conventional NN calculation when a large linear system size L is considered. The method employed here provides an extremely resource-efficient route for applying NN techniques to study the critical behaviors of higher-dimensional systems.
Related
- Accurate ground-state entropies from population Monte Carlo: The antiferromagnetic Ising model on the Shastry-Sutherland lattice
- Critical Ising Model on the Periodic Cubic Lattice (ℤ/Lℤ)3
- Phase transitions in coupled Ising chains and SO(N)-symmetric spin chains
- Phase transitions of a cubic Casimir matrix model on the fuzzy sphere
- Vector chiral order and dynamical quantum phase transitions in an Ising chain with dimerized anisotropic Gamma interaction
BibTeX
@misc{huang2026phase,
title = {{Phase transitions of the antiferromagnetic $J_1$-$J_2$-$J_3$ Ising model on the cubic lattice}},
author = {Kai-Wei Huang and Chien-Ting Chen and Shang-Wei Li and Fu-Jiun Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25884},
eprint = {2610.25884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25884},
}
RIS
TY - UNPB
TI - Phase transitions of the antiferromagnetic J_1-J_2-J_3 Ising model on the cubic lattice
AU - Kai-Wei Huang
AU - Chien-Ting Chen
AU - Shang-Wei Li
AU - Fu-Jiun Jiang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25884
UR - https://arxiv.org/abs/2610.25884
AB - Motivated by the conflicting findings in prior studies regarding the nature of the phase transition for the three-dimensional antiferromagnetic J_1-J_2-J_3 Ising model on the cubic lattice with J_1 = J_2 = J_3 = 1.0, in this study we conduct a detailed investigation of this model using both Monte Carlo simulations and neural networks (NN). Here J_1 and J_2 are the intralayer nearest-neighbor and next-nearest-neighbor couplings, respectively, and J_3 is the nearest-neighbor interlayer interaction. By investigating the data obtained from much larger lattices than those used in previous studies, we find that the phase transition for J_1 = J_2 = J_3 = 1.0 is second order without any ambiguity. Hence we bring a resolution to this debate. Apart from J_1 = J_2 = J_3 = 1.0, we study the critical phenomenon associated with J_2/J_1 = 4/7 and J_3 = J_1 = 1.0 as well. In addition, by employing a dedicated training and testing strategy, our NN computation not only is much more efficient than those utilizing the standard procedures commonly used in the literature, but also requires only a per-mille fraction of the storage capacity needed by a conventional NN calculation when a large linear system size L is considered. The method employed here provides an extremely resource-efficient route for applying NN techniques to study the critical behaviors of higher-dimensional systems.
ER -