Ising model on a hyperbolic plane with a boundary

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.

10 pages, 9 figures, to appear in Phys. Rev. E

References in corpus (5)

• Periodic boundary conditions on the pseudosphere
• Percolation on hyperbolic lattices
• Monte-Carlo simulation study of the two-stage percolation transition in enhanced binary trees
• Phase transition of $q$-state clock models on heptagonal lattices
• Bounds of percolation thresholds in the enhanced binary tree

Cited by in corpus (7)

• Holography on tessellations of hyperbolic space
• Crossing on hyperbolic lattices
• Scaling of Clusters near Discontinuous Percolation Transitions in Hyperbolic Networks
• Classification of critical phenomena in hierarchical small-world networks
• From explosive to infinite-order transitions on a hyperbolic network
• Critical Phenomena in Hyperbolic Space
• Upper transition point for percolation on the enhanced binary tree: A sharpened lower bound