Short-time relaxation of the Ising model on curved surfaces

Abstract We investigate the dynamic critical exponent of a two-dimensional Ising model defined on a curved surface with a constant negative curvature. By means of the short-time relaxation method, we find that a non-zero curvature of the underlying surface engenders a quantitative alternation of the dynamic exponent from the known value for the planar Ising model. This indicates the occurrence of a novel dynamic universality class of the Ising model induced by the negative surface curvature.