title: Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices.
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.
authors.affiliation: Institute of Physics, Slovak Academy of Sciences, SK-845 11 Bratislava, Slovakia.
authors.forename: Andrej
authors.initials: A
authors.lastname: Gendiar
authors.forename: Roman
authors.initials: R
authors.lastname: Krcmar
authors.forename: Sabine
authors.initials: S
authors.lastname: Andergassen
authors.forename: Michal
authors.initials: M
authors.lastname: Daniška
authors.forename: Tomotoshi
authors.initials: T
authors.lastname: Nishino