Scaling Hysteresis of Dynamical Transition in Dilute Heisenberg Spin Systems

The Monte Carlo method was employed to perform a numerical simulation for a classical discrete diluted Heisenberg spin system driven by an oscillating external magnetic field. To form the diluted spin system based on the isotropic Heisenberg model, we introduced in the Hamiltonian of the typical Heisenberg model both a random uniaxial anisotropy energy term characterizing an amorphous state with a proportion X and a deterministic uniaxial or triaxial anisotropy energy term representing a crystalline state with a proportion 1-X as balance. The dynamical transitional behavior of the diluted spin system mentioned above, i.e. the hysteresis loop scaled against parameter X and random uniaxial as well as deterministic uniaxial/triaxial anisotropy constants D and A, respectively, was studied in detail. For the first time, a scaling formula correlating the hysteresis loop area A(area) with the parameters X, A, and D has been put forward by us as A(area) similar to A(delta)D(eta)X(sigma). The main conclusions are summarized in the following: (i) At a specific value X (defined as X-min), the investigated spin system gains the minimal hysteresis, which has been supported experimentally in another part of our investigation. (ii) The scaling exponents delta, eta, and sigma of the diluted spin system are constants independent of the lattice size, the frequency, the amplitude of the driving field, and the temperature of system. The sum of exponents delta + eta (approximate to 0.9) of the diluted spin system equals the exponents delta, eta of sigma single either deterministic uniaxial/triaxial or random uniaxial anisotropy spin system. (iii) The specific value Xmin versus the logarithm of the ratio AID shows a peculiar sigmoidal trend.