Non-equilibrium critical relaxation of the three-dimensional Ising model

Abstract

The non-equilibrium relaxation process at the critical point is studied using Monte Carlo simulation for the ferromagnetic Ising model on a cubic lattice. It was observed that the time-dependent magnetization decayed following a power law t -λ from the all-up initial condition. Three kinds of single-spin-flip dynamics were studied for several lattices up to 1536 3. The system size dependences are also studied. The value of λ was estimated to be 0.250(2). This value of λ leads to the estimation of the dynamical exponent z to be 2.06(2) if we assume λ= β zν , where β and ν denote the critical exponents for spontaneous magnetization and correlation length in equilibrium state, respectively, and β ν =0.515 . The result of the non-equilibrium relaxation in the ordered phase is also given.