HIGH-TEMPERATURE SERIES EXPANSION FOR THE RELAXATION-TIMES OF THE 2-DIMENSIONAL ISING-MODEL

We derive the high temperature series expansions for the two relaxatio n times of the single spin-flip kinetic Ising model on the square latt ice. The series for the linear relaxation time tau(l) is obtained with 20 non-trivial terms, and the analysis yields 2.183 +/- 0.005 as the value of the critical exponent Delta(l), which is equal to the dynamic al critical exponent 2 in the two-dimensional case. For the non-linear relaxation time we obtain 15 non-trivial terms, and the analysis lead s to the result Delta(nl) = 2.08 +/- 0.07. The scaling relation Delta( l) - Delta(nl) = beta (beta being the exponent of the order parameter) seems to be fulfilled, though the error bars of Delta(nl) are still q uite substantial. In addition, we obtain the series expansion of the l inear relaxation time on the honeycomb lattice with 22 non-trivial ter ms. The result for the critical exponent is close to the value obtaine d on the square lattice, which is expected from universality.