Analysis of the finite-size effect of the long-range Ising model under Glauber dynamics

Abstract We considered a long-range Ising model under Glauber dynamics and calculated the difference from mean-field approximation in finite-size system using perturbation theory. To deal with Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, we assumed that certain types of extensive properties have Gaussian distribution, which turned out to be equivalent Kirkwood superposition within range first-order perturbation. After several calculations, ordinary differential equations describe time development two-body correlation were derived. This discussion is generalization our previous study developed similar consideration on infinite-range model. The results calculation fit those numerical simulations for case decay interaction was sufficiently slow; however, they exhibited different behaviors when became rapid.