Critical dynamics of random magnetic systems

Alfred Nash

Dudka, Folk, Yurij V. Holovatch +1 more

We study the purely relaxational critical dynamics with non-conserved order parameter (model A critical dynamics) for three-dimensional magnets with disorder in a form of the random anisotropy axis.For the random axis anisotropic distribution, the static asymptotic critical behaviour coincides with that of random site Ising systems.Therefore the asymptotic critical dynamics is governed by the dynamical exponent of the random Ising model.However, the disorder effects considerably the dynamical behaviour in the non-asymptotic regime.We perform a field-theoretical renormalization group analysis within the minimal subtraction scheme in two-loop approximation to investigate asymptotic and effective critical dynamics of random anisotropy systems.The results demonstrate the non-monotonic behaviour of the dynamical effective critical exponent z eff .

Fumihiko Tanaka

Equilibrium properties of the phase transition of a ferromagnetic spin system under a quenched random magnetic field are briefly summarized. Based upon a path integral formulation for stochastic processes, the n→0 method of replica is extended to treat critical relaxation of quenched random spin systems. As an application, the dynamic scaling hypothesis is examined for the random field problem by means of 1/m-expansion method (m; the number of order parameter components) and the renormalization group method near 6 space dimensions. It is shown that d→d−2 rule does not hold for the dynamic critical exponent of the characteristic frequency.

Amnon Aharony A

Hazime Mori, Hisao Okamoto

He-Ping Ying, Kenji Harada

The critical behavior in the short-time dynamics for the random-bond Potts ferromagnet in two dimensions is investigated by short-time dynamic Monte Carlo simulations. The numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic, which is used to estimate the critical exponents straight theta,beta/nu, and z, for quenched disordered systems from the power-law behavior of the kth moments of magnetization.