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Two temperature scales in the Ising model on the $\{5,4\}$ hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order — arXiv:2609.29323

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.29323
License (as archived): CC0-1.0
Archived: 2026-10-08T08:00:12.526Z
SHA-256 of the archived text: 04bd220086a4fc058246a1b5c5a795efa41266d58a4c29f5a9440e833a038b3d
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How to cite

Two temperature scales in the Ising model on the $\{5,4\}$ hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order — arXiv:2609.29323 — arXiv (en), https://arxiv.org/abs/2609.29323 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_011b2ee2cf71 (Metraipolis archive dc_011b2ee2cf71, sha256 04bd220086a4fc058246a1b5c5a795efa41266d58a4c29f5a9440e833a038b3d)

BibTeX

@misc{dc011b2ee2cf71,
  title = {Two temperature scales in the Ising model on the $5,4$ hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order — arXiv:2609.29323},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.29323},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_011b2ee2cf71; sha256 04bd220086a4fc058246a1b5c5a795efa41266d58a4c29f5a9440e833a038b3d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.29323. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

On the $\{5,4\}$ hyperbolic lattice, the outermost generation holds 73\% of the sites at all system sizes, making macroscopic averages strictly boundary-dependent. We study the ferromagnetic Ising model on this geometry with free boundaries by Monte Carlo simulation, demonstrating that conventional observables cease to identify a single critical scale. Instead, the finite lattices are organized by two distinct temperature scales. The susceptibility maximum identifies the lower transition scale at $T_{c2}=1.4782(15)J/k_{B}$ without extrapolation. However, the order-parameter distribution lacks a conventional fixed point at this scale. A distinct pseudocritical scale emerges instead at $T^{*}\simeq1.67(3)$ inside the boundary-sensitive intermediate phase, where Binder cumulant curves cross and effective exponents are compatible with mean-field criticality. Between $T_{c2}$ and $T^{*}$, the interior amplifies boundary fluctuations into induced order. Furthermore, because the volume grows exponentially with depth, finite-size scaling must be formulated in the generation index rather than the total number of sites. The lack of asymptotic power-law convergence in the scaling stretch confirms through an independent observable that $T^{*}$ is a finite-size crossover rather than a thermodynamic fixed point. Finally, by applying a coherent field to the outermost generation alone, we recover the upper thermodynamic transition at $T_{pt}=2.81(1)J/k_{B}$, demonstrating that it remains accessible under an appropriate boundary perturbation.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-25 in cond-mat.stat-mech).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech).
Pagina del lavoro: https://arxiv.org/abs/2609.29323 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T07:16:42.721Z dalla pagina https://arxiv.org/catchup/cond-mat.stat-mech/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).