Ising model on a hyperbolic lattice studied by the corner transfer matrix renormalization group method

DOI10.1088/1751-8113/41/12/125001zbMATH Open1189.82028arXiv0712.0461OpenAlexW3101502065MaRDI QIDQ5458981

Author name not available (Why is that?)

Publication date: 24 April 2008

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: We study two-dimensional ferromagnetic Ising model on a series of regular lattices, which are represented as the tessellation of polygons with p>=5 sides, such as pentagons (p=5), hexagons (p=6), etc. Such lattices are on hyperbolic planes, which have constant negative scalar curvatures. We calculate critical temperatures and scaling exponents by use of the corner transfer matrix renormalization group method. As a result, the mean-field like phase transition is observed for all the cases p>=5. Convergence of the calculated transition temperatures with respect to p is investigated towards the limit p->infinity, where the system coincides with the Ising model on the Bethe lattice.

Full work available at URL: https://arxiv.org/abs/0712.0461

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (3)

Replicated transfer matrix analysis of Ising spin models on  small world  lattices ⋮ The Ising model on hyperlattices ⋮ Iterated star–triangle transformation on inhomogeneous 2D Ising lattices

Recommendations

• Phase transition for the Ising model on the critical Lorentzian triangulation 👍 👎
• Ising models on the Lobachevsky plane 👍 👎
• Corner transfer matrices for the Ising model 👍 👎
• Ising models on hyperbolic graphs 👍 👎
• CONFORMAL PROPERTIES OF CRITICAL ISING MODEL CORNER TRANSFER MATRICES 👍 👎
• The Ising model on hyperlattices 👍 👎
• Transfer Matrix Study of Finite-size Corrections in the 2D Ising Model 👍 👎
• A new approach to real space renormalization group treatment of Ising model for square and simple cubic lattice 👍 👎
• Ising models on hyperbolic graphs. II 👍 👎
• Renormalization group maps for Ising models in lattice-gas variables 👍 👎

This page was built for publication: Ising model on a hyperbolic lattice studied by the corner transfer matrix renormalization group method

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5458981)