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

Andrej Gendiar, Roman Krcmar, Sabine Andergassen, Michal Daniška, and Tomotoshi Nishino
Phys. Rev. E 86, 021105 – Published 6 August 2012

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.

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  • Received 16 May 2012

DOI:https://doi.org/10.1103/PhysRevE.86.021105

©2012 American Physical Society

Authors & Affiliations

Andrej Gendiar1, Roman Krcmar2, Sabine Andergassen3, Michal Daniška1, and Tomotoshi Nishino4

  • 1Institute of Physics, Slovak Academy of Sciences, SK-845 11, Bratislava, Slovakia
  • 2Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig, Germany
  • 3Faculty of Physics, University of Vienna, Boltmanngasse 5, A-1090 Vienna, Austria
  • 4Department of Physics, Graduate School of Science, Kobe University, Kobe 657-8501, Japan

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Vol. 86, Iss. 2 — August 2012

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