Random loop representations for quantum spin systems [PDF]
Daniel UeltschiWe describe random loop models and their relations to a family of quantum spin systems on finite graphs. Spin correlations are given by loop correlations. Decay of correlations is proved in 2D-like graphs, and occurrence of macroscopic loops is proved in the cubic lattice in dimensions 3 and higher. A phase transition with magnetic long-range order is proved for SU(2)-invariant models of spin-1.View original: http://arxiv.org/abs/1301.0811
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