Investigates the bicritical dynamics of one-dimensional bond-diluted kinetic Ising models in the percolation limit at criticality. A wide class of single-spin-flip dynamics is applied and domain boundary diffusion arguments are used to identify the dominant processes producing flipping of the ordered finite chain segments constituting the diluted chain. Exact expressions for the rate of flip as a function of length of segment are obtained and are used to derive corresponding expressions for the decay of equilibrium correlations, and of the magnetisation (from a non-equilibrium uniformly magnetised initial state) in the chain. The results are in agreement with those of earlier rigorous calculations restricted to the special case of Glauber dynamics.
Single-time and two-correlators are computed exactly in the
1D Glauber-Ising model after a quench to zero temperature and on a periodic chain of finite length
N, using a simple analytical continuation technique. Besides the general confirmation of finite-size scaling in non-equilibrium dynamics, this allows to test the scaling behaviour of the plateau height
C∞(2) to which the two-time auto-correlator converges, when deep into the finite-size regime.
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of phase transition and critical behaviour. Branching annihilating random walks with an even number of offspring (on the part of the ferromagnetic domain boundaries), is a decisive process in forming the steady state of the system for a range of parameters, in the family of models considered. A wide variety of quantities characterize the critical behaviour of the system. Results of computer simulations and of a generalized mean field theory are presented and discussed.
The crossover between quasiequilibrium and nonequilibrium spin-glass dynamics has been studied in Monte Carlo simulations of two- and three-dimensional short-range Ising spin-glass systems. The spin system was quenched in zero field to a low temperature T. After equilibrating for a time
tw, a weak magnetic field was applied and the time dependence of the magnetization M(t) and the spin autocorrelation function q(t) was studied. Our results show that the relaxation rate S(t)=\ensuremath{\partial}M(t)/\ensuremath{\partial}
log10(t) exhibits a maximum at t\ensuremath{\approxeq}
tw. If the temperature is lowered or raised, immediately prior to the field application, the apparent age (
ta) of the system, as defined by the maximum in relaxation rate, is shifted to longer or shorter time scales, respectively. No significant differences between the aging behavior in two and three dimensions are found. The relation \ensuremath{\chi}(t)=[1-q(t)]/T holds only for short time scales (t\ensuremath{\ll}
tw), clear deviations are found at longer time scales (t>
tw). Since this relation should according to the fluctuation-dissipation theorem hold for a system in equilibrium, this result is interpreted as an indication of a crossover between equilibrium and nonequilibrium dynamics. Our results are qualitatively in agreement with experiments as well as with theoretical models for the nonequilibrium spin-glass dynamics.
A family of nonequilibrium kinetic Ising models, introduced earlier, evolving under the competing effect of spin flips at zero temperature and nearest-neighbour random spin exchanges, is further investigated. By increasing the range of spin exchanges and/or their strength the nature of the phase transition 'Ising-to-active' becomes of (dynamic) mean-field type and a first-order tricritical point is located at the Glauber ( delta =0) limit. Corrections to the mean-field theory are evaluated up to sixth order in a cluster approximation and found to give good results concerning the phase boundary and the critical exponent beta of the order parameter which is obtained as beta approximately=1.0.
By means of Monte Carlo simulations on the three-dimensional Ising spin-glass model, we have studied aging phenomena with various temperature(
T)-change protocols. Particularly, a
T-shift protocol, in which a system is first quenched to and aged for a period
tw1 at a temperature
T1, and subsequently aged at a new temperature
T2 is closely investigated. Most importantly, the mean size of domains, which is extracted from the replica-overlap function, was found to grow monotonically without any appreciable decrease by the
T-change. We also found the relaxation of energy density and spin auto-correlation function during the
T-shift process can be explained within the following picture: the dynamics finally crossovers to an isothermal aging of
T2 at around
t2≃tw1(eff) after the
T-change, where
tw1(eff) is an effective waiting time related with
tw1, but in the transient regime
t2<tw1(eff), adjustment of the population of thermally active droplets from that at
T1 to
T2 takes place very slowly. Implications of the results on aging phenomena in other
T-change protocols such as
T-cycling and continuous
T-change with an intermittent stop observed by simulations as well as experiments are discussed.