Study of the nonequilibrium critical quenching and the annealing dynamics for the long-range Ising model in one dimension

Abstract

Extensive Monte Carlo simulations are employed in order to study the dynamic critical behaviour of the one-dimensional Ising magnet, with algebraically decaying long-range interactions of the form rac{1}{r^{d+sigma}} with sigma=0.75. The critical temperature, as well as the critical exponents, are evaluated from the power-law behaviour 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 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 scalinganalysis of data measured with different truncated-interaction range.All the estimated static critical exponents (gamma / u, eta / u, and 1/ u) are in good agreement with Renormalization Group (RG)results and previously reported numerical data obtained under equilibrium conditions. On the other hand, the dynamic exponent of the initial increase of the magnetization (heta) was close to RG predictions. However, the dynamic exponent z of the time correlation length is slightly different than the RG results likely due to the fact that either it may depend on the specific dynamics used or because the two-loop expansion used in the RG analysis may be insufficient.