Dynamic scaling in pure and dilute systems

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Aleksandr Krinitsyn +3 more

Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations p=0.95 and 0.8 at criticality. In contrast to studies of the critical behavior of the pure systems by the short-time dynamics method, our investigations of site-diluted Ising model have revealed three stages of the dynamic evolution characterizing a crossover phenomenon from the critical behavior typical for the pure systems to behavior determined by the influence of disorder. The static and dynamic critical exponents are determined with the use of the corrections to scaling for systems starting separately from ordered and disordered initial states. The obtained values of the exponents demonstrate a universal behavior of weakly site-diluted Ising model in the critical region. The values of the exponents are compared to results of numerical simulations which have been obtained in various works and, also, with results of the renormalization-group description of this model.

Robin B. Stinchcombe

L. Wojtczak, B. Mrygoń

Robin B. Stinchcombe

A lattice rescaling method is applied to the equations of motion of the dilute Heisenberg chain and leads via a probabilistic integral equation to an iterative map for the characteristic frequency $\ensuremath{\beta}$ and concentration $p$. Dilution induces a crossover in the $\ensuremath{\beta}$ scaling from "chaotic" (ergodic and mixing) behavior, corresponding to the sampling of the pure band, to periodic orbits corresponding to isolated cluster response. A dynamic scaling form is obtained for the critical dynamics by fixed-point analysis.

Ivan S Popov, Anna P Popova, Pavel Vladimirovich Prudnikov +1 more

Structural disorder in two-dimensional XY-model creates an anomalous slowing down in the process of critical relaxation. Dynamic dependences of the correlation length ξ ( t ) show slow growth with an "effective" dynamical critical exponent z > 2. For a pure system, it has been shown that a detailed consideration of the vortex dynamics leads to deviations from the known dependence ξ ( t ) ∼ ( t /ln t ) 1/2 .

Wilhelm Brenig