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A general framework for crystallization in maximal hard-core models

  • Alexander Barg
  • Qidong He
  • Geyang Wang
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Abstract

We study general maximal hard-core models on periodic lattice-type graphs. While for standard models, phase coexistence may arise for high activity, for maximal models this behavior may occur also for sufficiently low activity values. Relying on the concept of volume allocation, we develop a {\em unified set of assumptions} that imply the Peierls condition, a convergent cluster expansion for the partition function, and hence the conclusions of Pirogov-Sinai theory for this class of models. We further check these assumptions for a number of examples including standard lattice-type periodic graphs, proving crystallization for both high and low activity. We also derive estimates for the values of activity that bound the phase coexistence regions in the phase diagram, rewriting for this purpose the proof of a technical result in the derivation of Pirogov-Sinai theory.

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Cite

BibTeXRIS
BibTeX
@misc{barg2026general,
  title = {{A general framework for crystallization in maximal hard-core models}},
  author = {Alexander Barg and Qidong He and Geyang Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11042},
  eprint = {2610.11042},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11042},
}
RIS
TY  - UNPB
TI  - A general framework for crystallization in maximal hard-core models
AU  - Alexander Barg
AU  - Qidong He
AU  - Geyang Wang
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11042
UR  - https://arxiv.org/abs/2610.11042
AB  - We study general maximal hard-core models on periodic lattice-type graphs. While for standard models, phase coexistence may arise for high activity, for maximal models this behavior may occur also for sufficiently low activity values. Relying on the concept of volume allocation, we develop a {\em unified set of assumptions} that imply the Peierls condition, a convergent cluster expansion for the partition function, and hence the conclusions of Pirogov-Sinai theory for this class of models. We further check these assumptions for a number of examples including standard lattice-type periodic graphs, proving crystallization for both high and low activity. We also derive estimates for the values of activity that bound the phase coexistence regions in the phase diagram, rewriting for this purpose the proof of a technical result in the derivation of Pirogov-Sinai theory.
ER  -