PreprintCC BY 4.0arXiv
Phase transition in the antiferromagnetic Ising model with external field
Abstract
Consider the nearest-neighbor antiferromagnetic Ising model on ℤd, d≥2, at inverse temperature β and in a uniform external field h. Let βc(d) be the critical inverse temperature of the zero-field Ising model. We prove that for every β>βc(d), the Gibbs state is not unique whenever |h| is sufficiently small. This extends a previous result of Dobrushin (1968) from sufficiently large β to every β>βc(d).
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BibTeX
@misc{jiang2026phase,
title = {{Phase transition in the antiferromagnetic Ising model with external field}},
author = {Jianping Jiang and Sike Lang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05184},
eprint = {2610.05184},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05184},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phase transition in the antiferromagnetic Ising model with external field
AU - Jianping Jiang
AU - Sike Lang
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05184
UR - https://arxiv.org/abs/2610.05184
AB - Consider the nearest-neighbor antiferromagnetic Ising model on ℤ^d, d≥2, at inverse temperature β and in a uniform external field h. Let β_c(d) be the critical inverse temperature of the zero-field Ising model. We prove that for every β>β_c(d), the Gibbs state is not unique whenever |h| is sufficiently small. This extends a previous result of Dobrushin (1968) from sufficiently large β to every β>β_c(d).
ER -