Geometric effects on critical behaviours of the Ising model

Details Geometric effects on critical behaviours of the Ising model Geometric effects on critical behaviours of the Ising model

2005-11-22

arxiv.org/abs/cond-mat/0511539v2

Physics

Condensed Matter

Statistical Mechanics

16 pages, 6 figures, to appear in J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/39/18/010

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic susceptibility and the correlation length deviate from those for the Ising lattice model on a flat plane. Furthermore, when reducing the effects of boundary spins, the values of the critical exponents tend to those derived from the mean field theory. These findings evidence that the underlying geometric character is responsible for the critical properties the Ising model when the lattice is embedded on negatively curved surfaces.

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