Critical Relaxation of Stochastic lsing Model

A markoffian stochastic model of interacting Ising spins is discussed near its critical point. The long time behavior of relaxation of its magnetization and energy is investigated near T c by the use of high-temperature series expansion and the ratio method. The numerical estimate of the critical exponent Δ M M of slowing down of magnetization is made, the results of which show Δ M M ≃2 for the simple square and triangular lattices, and Δ M M ≃1.4 for the simple cubic lattice. The exponent Δ E E of slowing down of energy is also estimated, which gives the result Δ E E ≃2 for the simple square and triangular lattices. The method to derive high-temperature expansion of an n -spin correlation function <σ 1 σ 2 …σ n > for an Ising model of spin 1/2 by the use of an equation of detailed balance is presented and applied to these estimates.