Study of the Nonequilibrium Critical Quenching and Annealing Dynamics for the Long-Range Ising Model

Extensive Monte Carlo simulations are employed in order to study the dynamic critical behavior of the one-dimensional Ising magnet, with algebraically decaying long-range interactions of the form $\frac{1}{r^{d+\sigma}}$, with $\sigma=0.75$. The critical temperature, as well as the critical exponents, is evaluated from the power-law behavior of suitable physical observables when the system is quenched from uncorrelated states, corresponding to infinite temperature, to the critical point. These results are compared with those obtained from the dynamic evolution of the system when it is suddenly annealed at the critical point from the ordered state. Also, the critical temperature in the infinite interaction limit is obtained by means of a finite-range scaling analysis of data measured with different cutoffs of the interaction range. All the estimated static critical exponents ($\gamma /\nu$, $\beta /\nu$, and $1/\nu$) are in good agreement with Renormalization Group (RG) predictions and previously reported numerical data obtained under equilibrium conditions. It is found that the dynamic exponent $z$ is different for quenching and annealing experiments, most likely due to the influence of the Kosterlitz-Thouless transition occurring at relatively similar algebraic decay of the interactions with $\sigma =1$. However, for annealing experiments the measured exponent $z$ is close to the RG predictions. On the other hand, the relevant exponents of the dynamic behavior ($z$ and $\theta$) are slightly different than the RG predictions, most likely due to the fact that they may depend on the especific dynamics used (Metropolis in the present paper).