title: Mean-field universality class induced by weak hyperbolic curvatures.
abstract: Order-disorder phase transition of the ferromagnetic Ising model is investigated on a series of two-dimensional lattices that have negative Gaussian curvatures. Exceptional lattice sites of coordination number seven are distributed on the triangular lattice, where the typical distance between the nearest exceptional sites is proportional to an integer parameter n. Thus, the corresponding curvature is asymptotically proportional to -n(-2). Spontaneous magnetization and specific heat are calculated by means of the corner transfer matrix renormalization group method. For all the finite n cases, we observe the mean-field-like phase transition. It is confirmed that the entanglement entropy at the transition temperature is linear in (c/6)ln n, where c = 1/2 is the central charge of the Ising model. The fact agrees with the presence of the typical length scale n being proportional to the curvature radius.
authors.affiliation: Institute of Physics, Slovak Academy of Sciences, SK-845 11, Bratislava, Slovakia.
authors.forename: Andrej
authors.initials: A
authors.lastname: Gendiar
authors.affiliation: Institute of Physics, Slovak Academy of Sciences, SK-845 11, Bratislava, Slovakia.
authors.forename: Michal
authors.initials: M
authors.lastname: Daniška
authors.affiliation: Institute of Physics, Slovak Academy of Sciences, SK-845 11, Bratislava, Slovakia and Department of Physics, Graduate School of Science, Kobe University, Kobe 657-8501, Japan.
authors.forename: Roman
authors.initials: R
authors.lastname: Krčmár
authors.affiliation: Department of Physics, Graduate School of Science, Kobe University, Kobe 657-8501, Japan.
authors.forename: Tomotoshi
authors.initials: T
authors.lastname: Nishino
mesh_terms: D060328:Magnetic Phenomena; D008962:Models, Theoretical; D044367:Phase Transition; D044366:Transition Temperature