Issues concerning the kinetics of phase transitions are not well established for the cases where the order parameter remains conserved with time, particularly when the interatomic interactions are long-range in nature. Here we present results on structure, growth, and aging from Monte Carlo simulations of the two-dimensional long-range Ising model. In our computer simulations, random initial configurations, for $50:50$ compositions of up and down spins, mimicking high-temperature equilibrium states, have been quenched to temperatures inside the coexistence curve. Our analyses of the simulation data, for such a protocol, show interesting dependence of the aging exponent, $\lambda$, on $\sigma$, the parameter, within the Hamiltonian, that controls the range of interaction. These nonuniversal values of $\lambda$ are compared with a theoretical result for lower bounds. For this purpose, we extracted information on relevant aspects of structural properties during the evolution. To estimate $\lambda$, as is necessary, we also calculated the average domain size and analyzed its time dependence to obtain the growth exponent $\alpha$ which also is nonuniversal. The trends in the values of $\lambda$ and $\alpha$, as well as an anomaly in structure, suggest that a crossover from the long-range to the short-range variety occurs at $\sigma \simeq 1$. The location of this boundary and the nonuniversality provide a picture that is surprisingly different from that of the corresponding static critical phenomena. Furthermore, our results suggest an important scaling law combining $\alpha$ and $\lambda$.

Close

PrevNext

View figure in article

• Classical statistical mechanics
• Pattern formation
• Phase separation
• Phase transitions