Andrey N. Vakilov’s research while affiliated with Omsk State University and other places

We used a Monte Carlo simulation of the structurally disordered three dimensional Ising model. For the systems with spin concentrations p = 0.95, 0.8, 0.6 and 0.5 we calculated the correlation-length critical exponent ν by finite-size scaling. Extrapolations to the thermodynamic limit yield ν(0.95) = 0.705(5), ν(0.8) = 0.711(6), ν(0.6) = 0.736(6) and ν(0.5) = 0.744(6). The analysis of the results demonstrates the nonuniversality of the critical behavior in the disordered Ising model.

We used a Monte Carlo simulation of the structurally disordered three dimensional Ising model. For the systems with spin concentrations p = 0.95 ,0.8, 0.6 and 0.5 we calculated the correlation-length critical exponent ν by finite-size scaling. Extrapolations to the thermodynamic limit yield ν(0.95) = 0.705(5) ,ν(0.8) = 0.711(6), ν(0.6) = 0.736(6) and ν(0.5) = 0.744(6). These results are compatible with some previous estimates from a variety of sources. The analysis of the results demonstrates the nonuniversality of the critical behavior in the disordered Ising model.

We investigate the non-equilibrium critical evolution of statistical systems and describe of its some features, such as aging and violation of the fluctuation-dissipation theorem. We consider some theoretical results of computations for universal quantities that have been obtained in recent years, such as the exponents determining the scaling behavior of dynamic response and correlation functions and the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics. We derive our original Monte Carlo simulation results for 3D pure and diluted Ising models with Glauber and Metropolis dynamics. For these models, we analyze the influence of critical fluctuations, different non-equilibrium initial states, and the presence of nonmagnetic impurities on the two-time dependence of correlation and response functions on characteristic time variables, such as waiting time $t_{\rm w}$ and time of observation $t - t_{\rm w}$ with $t > t_{\rm w}$ . We discuss the obtained values of the non-equilibrium exponents for the autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio $X^{\infty }$ . Our simulation results demonstrate that the insertion of disorder leads to new values of $X^{\infty }$ with $X_{\rm diluted}^{\infty } > X_{\rm pure}^{\infty }$ .

It is considered the non-equilibrium critical evolution of three-dimensional pure and site-diluted spin systems described by Ising model from high-temperature initial state with displaying some features, such as ageing and violation of the fluctuation–dissipation theorem. The Monte Carlo simulation results obtained for systems with the spin concentration varying in a wide range are given.

The parallel-tempering method has been applied to numerically study the thermo- dynamic behavior of a three-dimensional disordered antiferromagnetic Ising model with random fields at spin concentrations corresponding to regions of both weak and strong structural disorder. An analysis of the low-temperature behavior of the model convincingly shows that in the case of a weakly disordered samples there is realized an antiferromagnetic ordered state, while in the region of strong structural disorder the effects of random magnetic fields lead to the realization of a new phase state of the system with a complex domain structure consisting of antiferromagnetic and ferromagnetic domains separated by regions of a spin-glass phase and characterized by a spinglass ground state. Studying the critical behavior of disordered systems with quenched structural defects is of a great theoretical and experimental interest since the majority of real solids contain quenched structural defects whose presence influences their thermodynamic characteristics and, in particular, substantially affects the behavior of the systems during phase transitions. It is known that the effect of quenched impurities manifests itself in the form of random disturbances of the local temperature in ferro and antiferromagnetic systems in the absence of an external magnetic field or in the form of random magnetic fields in antiferromagnetic systems in a uniform magnetic field. The investigations performed showed that in the first case the presence of quenched nonmagnetic impurity atoms changes the properties of only anisotropic Ising like magnets