Large cycles in random permutations related to the Heisenberg model

Abstract

We study the weighted version of the interchange process where a permutation receives weight ${\theta }^{\#\mathrm{cycles}}$. For $\theta =2$ this is Tóth's representation of the quantum Heisenberg ferromagnet on the complete graph. We prove, for $\theta >1$, that large cycles appear at `low temperature'.

11 pages

References in corpus (1)

• Decay of transverse correlations in quantum Heisenberg models

Cited by in corpus (3)

• The free energy in a class of quantum spin systems and interchange processes
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