V. V. Prudnikov

Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model

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.

Short-Time Critical Dynamics of the Three-Dimensional Systems with Long-Range Correlated Disorder

Monte Carlo simulations of the short-time dynamic behavior are reported for threedimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting separately from ordered and disordered initial states. The obtained values of the exponents are in good agreement with results of the field-theoretic description of the critical behavior of these models in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.

Computer simulation of the critical behavior of 3D disordered ising model

The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.

Static and dynamic critical properties of 3D systems with long-range correlated quenched defects

A field-theoretic description of static and purely relaxational dynamic critical behaviour of systems with quenched defects obeying power law correlations ~|x|-a for large separations x is given. Directly, for three-dimensional systems and for different values of the correlation parameter, 2 a3, a renormalization analysis of the scaling functions in the two-loop approximation is carried out, and the fixed points corresponding to the stability of various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by a double ,-expansion. The static and dynamic critical exponents in the two-loop approximation are calculated with the use of the Pade-Borel summation technique.

Calculations of the dynamical critical exponent using the asymptotic series summation method

We consider how the Padé-Borel, Padé-Borel-Leroy, and conformal mapping summation methods for asymptotic series can be used to calculate the dynamical critical exponent for homogeneous and disordered Ising-like systems.

Dimensional Effects in Ultrathin Magnetic Films

Dimensional effects in the critical properties of multilayer Heisenberg films have been numerically studied by Monte Carlo methods. The effect of anisotropy created by the crystal field of a substrate has been taken into account for films with various thicknesses. The calculated critical exponents demonstrate a dimensional transition from two-dimensional to three-dimensional properties of the films with an increase in the number of layers. A spin-orientation transition to a planar phase has been revealed in films with thicknesses corresponding to the crossover region.

Renormalization-group description of nonequilibrium critical short-time relaxation processes: A three-loop approximation

The influence of nonequilibrium initial values of the order parameter on its evolution at a critical point is described using a renormalization group approach of the field theory. The dynamic critical exponent θ of the short time evolution of a system with an n-component order parameter is calculated within a dynamical dissipative model using the method of Σ-expansion in a three-loop approximation. Numerical values of θ for three-dimensional systems are determined using the Padé-Borel method for the summation of asymptotic series.

Monte Carlo investigations of the influence of structural defects on aging effects and the violation of the fluctuation-dissipation theorem for a nonequilibrium critical behavior in the three-dimensional Ising model

The specific features of a nonequilibrium critical behavior in the three-dimensional structurally disordered Ising model have been studied numerically by the Monte Carlo method. An analysis of the two-time dependence of the autocorrelation function and the dynamic susceptibility for systems with spin concentrations p = 0.8 and 0.6 has revealed the aging effects, which are characterized by a slowing down of the relaxation of the system with an increase in the waiting time, and the violation of the fluctuation-dissipation theorem. The values of the universal limit of fluctuation-dissipation ratio for the considered systems have been obtained using the Monte Carlo method. It has been shown that the presence of structural defects in the system leads to an enhancement of the aging effects and to an increase of the values of the limit of fluctuation-dissipation ratio.

Calculation of the Fluctuation-Dissipation Ratio for the Nonequilibrium Critical Behavior of Disordered Systems

The values of a new universal parameter characterizing a nonequilibrium critical behavior, namely, the fluctuation-dissipation ratio specifying a fundamental relation between the dynamic response function and the correlation function, are calculated for the disordered three-dimensional Ising model. The analysis of the two-time dependence for autocorrelation functions and the ac susceptibility for the systems with spin densities p = 1.0, 0.8, and 0.6 shows the aging effects characterized by the anomalous slowing of relaxation in the system with the growth of the waiting time and the violation of the fluctuation-dissipation theorem. To improve the accuracy of the ac susceptibility calculations, the “thermal bath” technique has been used without introducing the applied magnetic field in the simulation. It has been shown that the structural defects lead to the pronounced enhancement of the aging effects.

Monte Carlo simulation of multilayer magnetic structures and calculation of the magnetoresistance coefficient

The Monte Carlo study of three-layer and spin-valve magnetic structures with giant magnetoresistance effects has been performed with the application of the Heisenberg anisotropic model to the description of the magnetic properties of thin ferromagnetic films. The dependences of the magnetic characteristics on the temperature and external magnetic field have been obtained for the ferromagnetic and antiferromagnetic configurations of these structures. A Monte Carlo method for determining the magnetoresistance coefficient has been developed. The magnetoresistance coefficient has been calculated for three-layer and spin-valve magnetic structures at various thicknesses of ferromagnetic films. It has been shown that the calculated temperature dependence of the magnetoresistance coefficient is in good agreement with experimental data obtained for the Fe(001)/Cr(001) multilayer structure and the CFAS/Ag/CFAS/IrMn spin valve based on the Co2FeAl0.5Si0.5 (CFAS) Heusler alloy.