Nonequilibrium relaxation of the two-dimensional Ising model: Series-expansion and Monte Carlo studies

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We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time t and by Monte Carlo simulation. Both the magnetization (m) and energy series are obtained up to 12-th order. An accurate estimate from series analysis for the dynamical critical exponent z is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, zₑff(t) = - 1/8 d ln t /d ln m, directly from a ratio of three-spin correlation to m. Extrapolation to t = infinity leads to an estimate z = 2.169 +/- 0.003.