Critical dynamics of the two-dimensional kinetic Ising model: High-temperature series analysis of the autorelaxation time

For the two-dimensional nearest-neighbor kinetic Ising model without conservation laws, we derive on the square lattice the high-temperature series expansion of the autorelaxation time, to the eleventh order. With use of ratio methods and Padé approximants, we obtain for the dynamical critical exponent ${\mathrm{\Delta }}_{\mathit{A}}$ the value 2.09±0.03, which implies the value 2.34±0.03 for the linear relaxation exponent z. This value is about 10% larger than several other recent estimates. This discrepancy is possibly due to the relatively small number of nonzero coefficients in the series expansion.