The Universality of the Critical Dynamics of the Kinetic Ising Model on the Regular Fractals

Abstract

The form of the universal scaling law of the critical dynamic exponent, , is found on a family of regular fractals by the exact TDRG method. Here, we generate a regular fractal by an anisotropic growing process. Identifying the growing probabilities as the interactions between Ising spins on the fractals, we map the growing probability clouds as a group of the anisotropic Ising Hamiltonians. Applying the RG transformations, we find that the systems of this group of Ising Hamiltonians can be described by two universal static correlation exponents and . So, the growing processes proposed by us capture the essential features in the directed DLA simulations. The studies about their critical dynamic behaviours reveal that unlike the one-dimensional chain the critical dynamics of the kinetic Ising model on the regular fractals is universal. The further discussions show that there is a universal scaling law form of the critical dynamic exponent of the kinetic Ising model, , on the site models of the regular fractals with . Meanwhile, we discuss Daniel Kandal's correction to the formula of the, critical dynamic exponent in the TDRG method and show that our TDRG calculations are exact.