Two temperature scales in the Ising model on the {5,4} hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order
Abstract
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 Tc2=1.4782(15)J/kB without extrapolation. However, the order-parameter distribution lacks a conventional fixed point at this scale. A distinct pseudocritical scale emerges instead at T*≃1.67(3) inside the boundary-sensitive intermediate phase, where Binder cumulant curves cross and effective exponents are compatible with mean-field criticality. Between Tc2 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 Tpt=2.81(1)J/kB, demonstrating that it remains accessible under an appropriate boundary perturbation.
Related
- Boundary Condition dependent Universality Classes on a Hyperbolic Lattice
- Hybrid Lattice Surgery between Smooth Boundaries
- Examples of Gribov copies in the presence of planar boundaries, and an emergent boundary gauge invariance in Yang-Mills theory
- Boundaries of the compact free boson through edge modes and boundary SymTFT
- Boundary One-Point Functions in the Open XXZ Spin Chain with Generic Integrable Boundaries
BibTeX
@misc{jaroszewicz2026temperature,
title = {{Two temperature scales in the Ising model on the $\5,4\$ hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order}},
author = {Sebastian Jaroszewicz and Nahuel Mendez and Maria P. Beccar-Varela and Maria C. Mariani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29323},
eprint = {2609.29323},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29323},
}
RIS
TY - UNPB
TI - Two temperature scales in the Ising model on the {5,4} hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order
AU - Sebastian Jaroszewicz
AU - Nahuel Mendez
AU - Maria P. Beccar-Varela
AU - Maria C. Mariani
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29323
UR - https://arxiv.org/abs/2609.29323
AB - 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^*≃1.67(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.
ER -