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Universal Critical Jump for Inverse-Square Ising Ferromagnets

  • Dyuman Bhattacharya
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Abstract

For every translation-invariant ferromagnetic Ising chain with n2Jn→ B>0, we prove 2βcBmc2=1, without restrictions on the finite core or the tail convergence rate. The proof bounds the energy of macroscopic interfaces and rules them out if the critical product exceeds one. Despite the nonzero jump, connected susceptibility is infinite both at criticality and in a neighboring ordered interval. At the critical coupling, the excess magnetization decays more slowly than any positive power of the field as the field tends to zero. We also prove the jump relation in continuous time, for a positive-Stieltjes class of Ohmic spin-boson models.

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Cite

BibTeXRIS
BibTeX
@misc{bhattacharya2026universal,
  title = {{Universal Critical Jump for Inverse-Square Ising Ferromagnets}},
  author = {Dyuman Bhattacharya},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36131},
  eprint = {2610.36131},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36131},
}
RIS
TY  - UNPB
TI  - Universal Critical Jump for Inverse-Square Ising Ferromagnets
AU  - Dyuman Bhattacharya
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.36131
UR  - https://arxiv.org/abs/2610.36131
AB  - For every translation-invariant ferromagnetic Ising chain with n^2J_n→ B>0, we prove 2β_cBm_c^2=1, without restrictions on the finite core or the tail convergence rate. The proof bounds the energy of macroscopic interfaces and rules them out if the critical product exceeds one. Despite the nonzero jump, connected susceptibility is infinite both at criticality and in a neighboring ordered interval. At the critical coupling, the excess magnetization decays more slowly than any positive power of the field as the field tends to zero. We also prove the jump relation in continuous time, for a positive-Stieltjes class of Ohmic spin-boson models.
ER  -