Dynamics in a long-range exchange model

A new Ising dynamics with long-range exchange is proposed in which the exchange probability is a power law function of the distance between exchanged spins. Using a coarse-grained picture, a generalized time-dependent Ginzburg-Landau (TDGL) equation is derived. We analyze the dynamics of a first-order phase transition and a second-order phase transition, and we obtain the scaling function for droplet size distribution and the exponent of critical slowing down, respectively.