Percolation transition in the Bose gas

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Abstract
The canonical partition function of a Bose gas gives rise to a probability distribution over the permutations of N particles. The author studies the probability and mean value of the cycle lengths in the cyclic permutations, their relation to physical quantities like pair correlations, and their thermodynamic limit. He shows that in the ground state of most interacting boson gases the mean cycle length diverges in the bulk limit and the particles form macroscopic cycles. In the free Bose gas Bose-Einstein condensation is accompanied by a percolation transition: the appearance of infinite cycle with nonvanishing probability.

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