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For Heisenberg spins (n D 3/ the low energy configurations have jˇj; j j; jıj 1; for n D 2, spins are coplanar and two coordinates are fixed: ' D ı D 0. 8) In this way, we discover contrasting behaviour for the two cases. With n D 3, the system explores all values of ˛ even in the low temperature limit. ˛/ approaches a sum of two delta functions, located at ˛ D 0 and ˛ D . Thus, order by disorder is absent for n D 3 but perfect for n D 2. Passing from a single cluster to an extended system, consider the sketch of phase space given in Fig.

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To decide whether the system displays order by disorder, we need to understand which of these two parts dominates. x/ on the ground state manifold by integrating over transverse fluctuations [9,10]. x0 / vanishes. x0 / is divergent. As for a cluster of four spins, behaviour depends on whether any such divergence is integrable. If it is, the system explores the whole of the ground state manifold in the low temperature limit, but if it is not, then those ground states with soft modes are selected by thermal fluctuations.

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Application of High Magnetic Fields in Semiconductor Physics LNP0177


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