Boundary Condition dependent Universality Classes on a Hyperbolic Lattice
Abstract
We study the ferromagnetic Ising model on finite hyperbolic tessellations of Euclidean AdS2 with open and wired boundary conditions. Because a finite fraction of spins remains at the boundary as the lattice grows, these conditions select distinct thermodynamic behaviours. In the {5,4} tessellation, Monte-Carlo simulations using efficient worm algorithms on open boundaries (OBC) yield a transition near βc J=0.632(3), with susceptibility data collapsing under scaling by the total number of spins N. The fitted finite-size exponents, 1/ν̅ ≃ 0.162 and γ/ν̅ ≃ 0.743, differ substantially from the mean-field volume scaling. Wired boundaries (WBC), which correlate boundary spins, instead show a transition around βc J=0.348(4) to an ordered phase consistent with the mean-field exponents. While the mean-field criticality with WBC is consistent with previous studies and with the suppression of independent boundary fluctuations, the OBC exponents hint at the presence of a new universality class. Results from other tessellations support the robustness of the observed scaling with OBC. We discuss a possible route to interpolate between the different boundary conditions. Our findings show that boundary dynamics must be specified when characterizing critical behaviour on hyperbolic lattices.
Related
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BibTeX
@misc{dey2026boundary,
title = {{Boundary Condition dependent Universality Classes on a Hyperbolic Lattice}},
author = {Pallabi Dey and Debasish Banerjee and Arnab Kundu and Ritam Sinha},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37325},
eprint = {2609.37325},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37325},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Boundary Condition dependent Universality Classes on a Hyperbolic Lattice
AU - Pallabi Dey
AU - Debasish Banerjee
AU - Arnab Kundu
AU - Ritam Sinha
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37325
UR - https://arxiv.org/abs/2609.37325
AB - We study the ferromagnetic Ising model on finite hyperbolic tessellations of Euclidean AdS_2 with open and wired boundary conditions. Because a finite fraction of spins remains at the boundary as the lattice grows, these conditions select distinct thermodynamic behaviours. In the {5,4} tessellation, Monte-Carlo simulations using efficient worm algorithms on open boundaries (OBC) yield a transition near β_c J=0.632(3), with susceptibility data collapsing under scaling by the total number of spins N. The fitted finite-size exponents, 1/ν̅ ≃ 0.162 and γ/ν̅ ≃ 0.743, differ substantially from the mean-field volume scaling. Wired boundaries (WBC), which correlate boundary spins, instead show a transition around β_c J=0.348(4) to an ordered phase consistent with the mean-field exponents. While the mean-field criticality with WBC is consistent with previous studies and with the suppression of independent boundary fluctuations, the OBC exponents hint at the presence of a new universality class. Results from other tessellations support the robustness of the observed scaling with OBC. We discuss a possible route to interpolate between the different boundary conditions. Our findings show that boundary dynamics must be specified when characterizing critical behaviour on hyperbolic lattices.
ER -