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

Author(s): A. Gendiar, R. Krcmar, S. Andergassen, M. Daniska, T. Nishino

Journal: Phys. Rev. E

Volume: 86

Page(s): 8

Year: 2012

DOI Number: 10.1103/PhysRevE.86.021105

Link: Link to publication

Abstract:

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.

Note: http://arxiv.org/abs/1205.3850

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