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PreprintarXiv licencearXiv

Typical periodic optimization and freezing phase transition: Dini potentials and beyond

  • Yunping Jiang
  • Zhiqiang Li
  • Yiqing Sun
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Abstract

We investigate the Typical Periodic Optimization (TPO) Conjecture and freezing phase transitions for Dini potentials and beyond. We show that the TPO conjecture fails already at Dini regularity. We identify a sharp regularity threshold for freezing phase transitions, which we call weak log-log Dini. Both results reveal the stability of aperiodic ground states. Moreover, we identify Dini regularity as the sharp threshold for a quantitatitve analog of the freezing phase transition.

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Cite

BibTeXRIS
BibTeX
@misc{jiang2026typical,
  title = {{Typical periodic optimization and freezing phase transition: Dini potentials and beyond}},
  author = {Yunping Jiang and Zhiqiang Li and Yiqing Sun},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31327},
  eprint = {2610.31327},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31327},
}
RIS
TY  - UNPB
TI  - Typical periodic optimization and freezing phase transition: Dini potentials and beyond
AU  - Yunping Jiang
AU  - Zhiqiang Li
AU  - Yiqing Sun
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31327
UR  - https://arxiv.org/abs/2610.31327
AB  - We investigate the Typical Periodic Optimization (TPO) Conjecture and freezing phase transitions for Dini potentials and beyond. We show that the TPO conjecture fails already at Dini regularity. We identify a sharp regularity threshold for freezing phase transitions, which we call weak log-log Dini. Both results reveal the stability of aperiodic ground states. Moreover, we identify Dini regularity as the sharp threshold for a quantitatitve analog of the freezing phase transition.
ER  -