Large cycles in random permutations related to the Heisenberg model
Jakob E. Björnberg · Chalmers Publication Library (Chalmers University of Technology) · 2015
We study the weighted version of the interchange process where a permutation receives weight theta(#cycles). For theta = 2 this is Toth's representation of the quantum Heisenberg ferromagnet on the complete graph. We prove, for theta > 1, that large cycles appear at 'low temperature'.