Numerical study on critical exponents of hyperbolic Ising lattice

The current work focuses on critical exponents of the two-dimensional ferromagnetic Ising model defined on the hyperbolic plane. The hyperbolic plane is a simply connected infinite surface in which the Gaussian curvature possesses a constant negative curvature at arbitrary points. This non-zero curvature changes the geometric symmetry of the embedded Ising lattice model, and thus possibly induces an alteration in the universality class of the system. To clarify this point, we establish regular heptagonal and triangular Ising lattices embedded in the hyperbolic plane, and extract a series of critical exponents by means of Monte Carlo simulations and the finite-size scaling analysis.