Hiroyuki Shima, Yasunori Sakaniwa
Published 2005-12-08, updated 2006-08-17Version 3
We investigate the dynamic critical exponent of the two-dimensional Ising model defined on a curved surface with constant negative curvature. By using the short-time relaxation method, we find a quantitative alteration of the dynamic exponent from the known value for the planar Ising model. This phenomenon is attributed to the fact that the Ising lattices embedded on negatively curved surfaces act as ones in infinite dimensions, thus yielding the dynamic exponent deduced from mean field theory. We further demonstrate that the static critical exponent for the correlation length exhibits the mean field exponent, which agrees with the existing results obtained from canonical Monte Carlo simulations.
Comments: 14 pages, 3 figures. to appear in J. Stat. Mech
Mean field theory of chaotic insect swarms
Renormalization group for $\varphi^4$-theory with long-range interaction and the critical exponent $η$ of the Ising model
Ising model with memory: coarsening and persistence properties
