Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices

The Ising model is studied on a series of hyperbolic two-dimensional lattices which are formed by tessellation of triangles on negatively curved surfaces. In order to treat the hyperbolic lattices, we propose a generalization of the corner transfer matrix renormalization group method using a recursi...

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Bibliographic Details
Published in:arXiv.org 2012-07
Main Authors: Gendiar, Andrej, Krcmar, Roman, Andergassen, Sabine, Daniska, Michal, Nishino, Tomotoshi
Format: Article
Language:English
Subjects:
Correlation analysis
Curvature
Euclidean geometry
Ising model
Lattices
Mathematical models
Phase transitions
Recursive methods
Tessellation
Transfer matrices
Transition points
Triangles
Two dimensional models
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Summary:The Ising model is studied on a series of hyperbolic two-dimensional lattices which are formed by tessellation of triangles on negatively curved surfaces. In order to treat the hyperbolic lattices, we propose a generalization of the corner transfer matrix renormalization group method using a recursive construction of asymmetric transfer matrices. Studying the phase transition, the mean-field universality is captured by means of a precise analysis of thermodynamic functions. The correlation functions and the density matrix spectra always decay exponentially even at the transition point, whereas power law behavior characterizes criticality on the Euclidean flat geometry. We confirm the absence of a finite correlation length in the limit of infinite negative Gaussian curvature.
ISSN:2331-8422
DOI:10.48550/arxiv.1205.3850