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arXiv · 1109.6227

Ising model on a hyperbolic plane with a boundary

Seung Ki Baek·Harri Mäkelä·Petter Minnhagen·Beom Jun Kim
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Abstract

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.

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Seung Ki Baek, Harri Mäkelä, Petter Minnhagen, Beom Jun Kim. 2011-09-28. Ising model on a hyperbolic plane with a boundary. https://doi.org/10.1103/physreve.84.032103

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