Novel scaling behavior of the Ising model on curved surfaces

Abstract

We demonstrate the nontrivial scaling behavior of Ising models defined on (i) a donut-shaped surface and (ii) a curved surface with a constant negative curvature. By performing Monte Carlo simulations, we find that the former model has two distinct critical temperatures at which both the specific heat $C(T)$ and magnetic susceptibility $\chi (T)$ show sharp peaks.The critical exponents associated with the two critical temperatures are evaluated by the finite-size scaling analysis; the result reveals that the values of these exponents vary depending on the temperature range under consideration. In the case of the latter model, it is found that static and dynamic critical exponents deviate from those of the Ising model on a flat plane; this is a direct consequence of the constant negative curvature of the underlying surface.

11 pages 5 figures

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Cited by in corpus (10)

• Critical behavior in spherical and hyperbolic spaces
• Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
• On topological spin excitations on a rigid torus
• Critical properties of the Ising model in hyperbolic space
• Heisenberg model on a space with negative curvature: topological spin textures on the pseudosphere
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Phase Transition of the Ising model on a Hyperbolic Lattice
• Tricritical point of J1-J2 Ising model on hyperbolic lattice
• Free Energy Analysis of Spin Models on Hyperbolic Lattice Geometries
• Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices