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

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Krcmar, Roman
Gendiar, Andrej
Ueda, Kouji
Nishino, Tomotoshi
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Abstract
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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.
Comment: 9 pages, 12 figures
Keywords
Condensed Matter - Statistical Mechanics
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