Weak-coupling selection and finite-torus entropy in the triangular Ising antiferromagnet
Abstract
An antiferromagnetic second-neighbor interaction favors stripe order in the triangular-lattice Ising antiferromagnet, but uniform stripes cannot satisfy odd periodic boundaries. At each fixed odd size L≥5, we minimize this interaction over the ground states of the zero-field nearest-neighbor model on an L× L torus. We prove a minimum total interface length of 4L and classify all L2(L2−1)/2 selected states. Under the uniform measure on these states, the area fractions of the three stripe orientations approach a uniform distribution over all nonnegative triples summing to one. Thus selection reduces an exponential degeneracy to polynomial growth, while the whole-sample orientation fractions remain broadly distributed. We also derive explicit two-sided entropy-density bounds for periodic spin ground states and honeycomb dimer coverings on M× N tori, where M,N are the periods along the two primitive lattice directions. For all M,N≥3, the errors relative to the bulk residual entropy are bounded by explicit constants times min(M,N)−2, without an aspect-ratio restriction. These bounds give finite-size accuracy guarantees and control the exponentially small fraction of unperturbed ground states that survive the selection.
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BibTeX
@misc{jiang2026weakcoupling,
title = {{Weak-coupling selection and finite-torus entropy in the triangular Ising antiferromagnet}},
author = {Weiqi Jiang and Pengcheng Hou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00154},
eprint = {2611.00154},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00154},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weak-coupling selection and finite-torus entropy in the triangular Ising antiferromagnet
AU - Weiqi Jiang
AU - Pengcheng Hou
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00154
UR - https://arxiv.org/abs/2611.00154
AB - An antiferromagnetic second-neighbor interaction favors stripe order in the triangular-lattice Ising antiferromagnet, but uniform stripes cannot satisfy odd periodic boundaries. At each fixed odd size L≥5, we minimize this interaction over the ground states of the zero-field nearest-neighbor model on an L× L torus. We prove a minimum total interface length of 4L and classify all L^2(L^2−1)/2 selected states. Under the uniform measure on these states, the area fractions of the three stripe orientations approach a uniform distribution over all nonnegative triples summing to one. Thus selection reduces an exponential degeneracy to polynomial growth, while the whole-sample orientation fractions remain broadly distributed. We also derive explicit two-sided entropy-density bounds for periodic spin ground states and honeycomb dimer coverings on M× N tori, where M,N are the periods along the two primitive lattice directions. For all M,N≥3, the errors relative to the bulk residual entropy are bounded by explicit constants times min(M,N)^−2, without an aspect-ratio restriction. These bounds give finite-size accuracy guarantees and control the exponentially small fraction of unperturbed ground states that survive the selection.
ER -