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Since our scheme neglects spin-orbit coupling, the orientation of the spin system remains unspecified by an undetermined global rotation. The indetermination in this rotation does not affect our results, except for the representation of the magnetization in Cartesian components in Figs. 4(a)-4(c). Furthermore, note that this condition restricts our investigation to relative orientations of local magnetizations at equal times.
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A video animation of our simulation is shown at http://cphys.s.kanazawa- u.ac.jp/~oda/o2.html.
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5 configurations were used to estimate 1(Q). The acceptance ratio in the Metropolis algorithm varied between 30% and 50%, depending on temperature. An increase by a factor of 10 in the number of Monte Carlo steps led to a 0.1% variation of I(0) at 54 K.
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