Novel scaling behavior of the Ising model on curved surfaces

[摘要] 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. (c) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2007-11-15

[效力级别]  Proceedings Paper

[关键词] Ising model;Monte Carlo simulation;phase transition;curved surface;critical exponent