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

Autor(en)

Andrej Gendiar, Roman Krcmar, Sabine Andergassen, Michal Daniska, Tomotoshi Nishino

Abstrakt

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.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Slovenian Academy of Sciences and Arts, Physikalisch-Technische Bundesanstalt, Kobe University

Journal

Physical Review E

Band

86

Anzahl der Seiten

8

ISSN

1539-3755

DOI

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

Publikationsdatum

2012

Peer-reviewed

Ja

ÖFOS 2012

103026 Quantenoptik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/55672a7a-3a3f-4bcd-b7af-03032bc3b3de