Universality of the Ising Model on Sphere-like Lattices

Details Universality of the Ising Model on Sphere-like Lattices Universality of the Ising Model on Sphere-like Lattices

1996-02-26

arxiv.org/abs/hep-lat/9602025v1

Phys.Rev. B54 (1996) 3434

Physics

High Energy Physics

High Energy Physics - Lattice

24 pages, LaTeX, 8 figures

Scientific paper

10.1103/PhysRevB.54.3434

We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes ranging up to O($10^5$) sites are simulated and finite size scaling is analyzed. The partition function zeros and the values of various cumulants at their respective peak positions are determined and they agree with the scaling behavior expected from universality with the Onsager solution on the torus ($\nu=1$). For the pseudocritical values of the coupling we find significant anomalies indicating a shift exponent $\neq 1$ for sphere-like lattice topology.

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