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

Abstract

Extensive Monte Carlo simulations are employed in order to study the dynamic critical behaviour ofthe one-dimensional Ising magnet, with algebraically decaying long-range interactions of the form1/rd + σ, withσ = 0.75. The critical temperature, as well as the critical exponents, are evaluated fromthe power-law behaviour of suitable physical observables when the system isquenched from uncorrelated states, corresponding to infinite temperature, tothe critical point. These results are compared with those obtained from thedynamic evolution of the system when it is annealed at the critical point fromthe ordered state. Also, the critical temperature in the infinite interaction limitis obtained by means of a finite-range scaling analysis of data measured withdifferent truncated interaction ranges. All the estimated static critical exponents (γ/ν,β/ν, and1/ν) are in good agreement with renormalization group (RG) results and previouslyreported numerical data obtained under equilibrium conditions. On the otherhand, the dynamic exponent of the initial increase of the magnetization (θ) was close to RG predictions. However, the dynamic exponentz of the time correlation length is slightly different to the RG results probably due to the factthat it may depend on the specific dynamics used or because the two-loop expansion usedin the RG analysis may be insufficient.