A hyperbolic plane can be modeled by a structure called the enhanced binary tree. We study the ferromagnetic Ising model on top of the enhanced binary tree using the renormalization-group analysis in combination with transfer-matrix calculations. We find a reasonable agreement with Monte Carlo calculations on the transition point, and the resulting critical exponents suggest the mean-field surface critical behavior.
@article{arxiv.1109.6227,
title = {Ising model on a hyperbolic plane with a boundary},
author = {Seung Ki Baek and Harri Mäkelä and Petter Minnhagen and Beom Jun Kim},
journal= {arXiv preprint arXiv:1109.6227},
year = {2015}
}