Linear and nonlinear critical slowing down in the kinetic Ising model: High-temperature series

The difference between the critical exponents (Δ(l) and Δ(nl)) of the linear and nonlinear relaxation times of the order parameter (τ(l) and τ(nl)) is investigated in the two-dimensional one-spin-flip kinetic Ising model. We have calculated the high-temperature series for τ(nl) up to ninth order and made use of the known series for τ(l) up to twelfth order. The series are analyzed by the ratio and the Padé-approximant methods. The correlation between the critical-point and critical-exponent estimates in the Padé approximants allows an improvement in the determination of Δ(l). The result, Δ(l)=2.125±0.01, is higher than previous estimates of 2.0 ± 0.05. The estimate of Δ(nl) is less precise but the result Δ(nl)=1.95±0.15 leads to the conclusion that Δ(l)≠Δ(nl) and that the difference between the two is of order β (critical index of the order parameter). This is in accord with the scaling prediction.