This paper presents the recent experimental results on development of an optical frequency standard based on ultra cold magnesium atoms with relative frequency uncertainty and long term stability at ...the level of Δv/v <10−16. We stabilized the frequency of our clock laser system at 655 THz to narrow Ramsey fringes in a time separated laser fields interacting with cooled Mg atoms localized in a magneto-optical trap (MOT). The intercombination line 1S0→3P1 was used as the reference for frequency stabilization. The results of stabilization were studied with femtosecond comb based on Ti:Sa laser.
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.
The influence of various initial magnetizations
m
0
and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. ...Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations
p
≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with
p
≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.
Simulation of critical relaxation of the magnetization in a three-dimensional Ising model diluted by quenched nonmagnetic impurity atoms is carried out. The cubic systems with linear size L 144 and ...spin concentrations p 0.95, 0.8, 0.6, and 0.5 are studied. The dynamical critical exponent z is determined by the Monte Carlo method combined with the dynamical renormalization group method. The obtained results are: z(p): z(0.95) 2.19 ± 0.07, z(0.8) 2.29 ± 0.06, z(0.6) 2.72 ± 0.08, and z(0.5) 2.75 ± 0.08.
The effect of different initial values
m
0
of magnetization and structural defects on the nonequilibrium critical behavior of the 3D Ising model have been analyzed numerically using the Monte Carlo ...method. Analysis of the two-time dependences of the autocorrelation function and dynamic susceptibility has revealed a substantial influence of the initial states on the aging effects that are characterized by anomalous retardation of relaxation and correlation in the system upon an increase in the waiting time. We have studied the violations of the fluctuation–dissipation theorem and calculated the limiting fluctuation–dissipation ratio. It is shown that in the nonequilibrium critical behavior of the 3D Ising model, two universality subclasses corresponding to the evolution of the system from the high-temperature (with
m
0
= 0) and low-temperature (with
m
0
= 1) initial states with the values of the limiting fluctuation–dissipation ratio typical of these states can be singled out.
The effect of various initial magnetizations
m
0
and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the ...time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization
m
0
These subclasses correspond to the system evolution from the high-temperature (
m
0
= 0) and low-temperature (
m
0
= 1) initial states with limit FDRs characteristic of these states.
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