1,721,000 research outputs found
Phase ordering in 3d disordered systems
No full textWe study numerically the phase-ordering kinetics of the site-diluted and bond-diluted Ising models after a quench from an infinite to a low temperature. We show that the speed of growth of the ordered domain's size is non-monotonous with respect to the amount of dilution D: starting from the pure case D = 0 the system slows down when dilution is added, as it is usually expected when disorder is introduced, but only up to a certain value D* beyond which the speed of growth raises again. We interpret this counterintuitive fact in a renormalization-group inspired framework, along the same lines proposed for the corresponding two-dimensional systems, where a similar pattern was observed
Condensation vs phase ordering in the dynamics of first-order transitions
No full textThe origin of the noncommutativity of the limits t-->infinity and N-->infinity in the dynamics of first-order transitions is investigated. In the large-N model, i.e., N-->infinity taken first, the low-temperature phase is characterized by condensation of the large-wavelength fluctuations rather than by genuine phase ordering as when t-->infinity is taken first. A detailed study of the scaling properties of the structure factor in the large-N model is carried out for quenches above, at, and below T-c. Preasymptotic scaling is found and crossover phenomena are related to the existence of components in the order parameter with different scaling properties. Implications for phase ordering in realistic systems are discussed
Slow relaxation in the large-N model for phase ordering
No full textThe basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large-N model through the exact separation of the order parameter into the sum of thermal and condensation components. The aging contribution in the response function chi(ag)(t,t(w)) is found to obey a pattern of behavior, under variation of dimensionality, qualitatively similar to the one observed in Ising systems. There exists a critical dimensionality (d=4) above which chi(ag)(t,t(w)) is proportional to the defect density rho(D)(t), while for d<4 it vanishes more slowly than rho(D)(t) and at d=2 does not vanish. As in the Ising case, this behavior can be understood in terms of the dependence on dimensionality of the interplay between the defect density and the effective response associated to a single defect
Comment on "Scaling of the linear response in simple aging systems without disorder"
No full textWe have repeated the simulations of Henkel, Paessens, and Pleimling (HPP) [Phys. Rev. E 69, 056109 (2004)] for the field-cooled susceptibility chi(FC)(t)-chi(0)similar to t(-A) in the quench of ferromagnetic systems to and below T-C. We show that, contrary to the statement made by HPP, the exponent A coincides with the exponent a of the linear response function R(t,s)similar to s(-(1+a))f(R)(t/s). We point out what are the assumptions in the argument of HPP that lead them to the conclusion A < a
Correction to scaling in the response function of the two-dimensional kinetic Ising model
No full textThe aging part R-ag(t,s) of the impulsive response function of the two-dimensional ferromagnetic Ising model, quenched below the critical point, is studied numerically employing an algorithm without the imposition of the external field. We find that the simple scaling form R-ag(t,s)=s(-(1+a))f(t/s), which is usually believed to hold in the aging regime, is not obeyed. We analyze the data assuming the existence of a correction to scaling. We find a=0.273 +/- 0.006, in agreement with previous numerical results obtained from the zero field cooled magnetization. We investigate in detail also the scaling function f(t/s) and we compare the results with the predictions of analytical theories. We make an ansatz for the correction to scaling, deriving an analytical expression for R-ag(t,s). This gives a satisfactory qualitative agreement with the numerical data for R-ag(t,s) and for the integrated response functions. With the analytical model we explore the overall behavior, extrapolating beyond the time regime accessible with the simulations. We explain why the data for the zero field cooled susceptibility are not too sensitive to the existence of the correction to scaling in R-ag(t,s), making this quantity the most convenient for the study of the asymptotic scaling properties
Influence of thermal fluctuations on the geometry of interfaces of the quenched Ising model
No full textWe study the role of the quench temperature T(f) in the phase-ordering kinetics of the Ising model with single spin flip in d=2,3. Equilibrium interfaces are flat at T(f)=0, whereas at T(f)>0 they are curved and rough (above the roughening temperature in d=3). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent z=2 of the size of domains L(t)similar to t(1/z) is unaffected by T(f), other exponents related to the interface geometry take different values at T(f)=0 or T(f)>0. For T(f)>0 a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at T(f)=0, to the asymptotic regime with curved interfaces characteristic of T(f)>0. Furthermore, it is shown that the roughening length, although subdominant with respect to L(t), produces appreciable correction to scaling up to very long times in d=2
The effective temperature in the quenching of coarsening systems to and to below Tc
No full textWe overview the general scaling behavior of the effective temperature in the que nches of simple non disordered systems, like ferromagnets, to and below . Emphasis is on the behavior as d imensionality is varied. Consequences on the shape of the asymptotic parametric representation are derived. In particu lar, this is always trivial in the critical quenches with . We clarify that the quench to at the lower critical dimensionality , cannot be regarded as a critical quench. Implications for the behavior of the exponent of the aging response function in the quenches below are developed
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