Ising model on a hyperbolic plane with a boundary

TL;DR

This paper investigates the ferromagnetic Ising model on a hyperbolic plane modeled by an enhanced binary tree, using renormalization-group and transfer-matrix methods, revealing mean-field surface critical behavior.

Contribution

It combines renormalization-group analysis with transfer-matrix calculations to study the Ising model on a hyperbolic plane, providing new insights into its critical behavior.

Findings

Agreement with Monte Carlo transition point

Critical exponents suggest mean-field surface behavior

Enhanced binary tree effectively models hyperbolic geometry

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.