On a model of random cycles

Abstract

We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with infinite, macroscopic cycles.

13 pages

References in corpus (2)

• Percolation transition in the Bose gas II
• The relation between Feynman cycles and off-diagonal long-range order

Cited by in corpus (10)

• Spatial random permutations and infinite cycles
• Spatial random permutations and Poisson-Dirichlet law of cycle lengths
• Spatial random permutations with small cycle weights
• Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
• Random permutations of a regular lattice
• Gibbs measures on permutations over one-dimensional discrete point sets
• Shift in critical temperature for random spatial permutations with cycle weights
• Split-and-Merge in Stationary Random Stirring on Lattice Torus
• Finite cycle Gibbs measures on permutations of ${\mathbb{Z}}^d$
• The model of interacting spatial permutations and its relation to the Bose gas