Survival of short-range order in the Ising model on negatively curved surfaces.
We examine the ordering behavior of the ferromagnetic Ising lattice model defined on a surface with a constant negative curvature. Small-sized ferromagnetic domains are observed to exist at temperatures far greater than the critical temperature, at which the inner-core region of the lattice undergoes a mean-field phase transition. The survival of short-range order at such high temperatures can be attributed to strong boundary-spin contributions to the ordering mechanism as a result of which boundary effects remain active even within the thermodynamic limit. Our results are consistent with the previous finding of disorder-free Griffiths phase that is stable at temperatures lower than the mean-field critical temperature.
Department of Applied Physics, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan.
Yasunori
Y
Sakaniwa
Hiroyuki
H
Shima