title: Length distributions in loop soups.
abstract: Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using CP(n-1) or RP(n-1) and O(n) σ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter θ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.
authors.affiliation: Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom.
authors.forename: Adam
authors.initials: A
authors.lastname: Nahum
authors.affiliation: Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom.
authors.forename: J T
authors.initials: JT
authors.lastname: Chalker
authors.affiliation: Departamento de Física-CIOyN, Universidad de Murcia, Murcia 30.071, Spain.
authors.forename: P
authors.initials: P
authors.lastname: Serna
authors.affiliation: Departamento de Física-CIOyN, Universidad de Murcia, Murcia 30.071, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Ortuño
authors.affiliation: Departamento de Física-CIOyN, Universidad de Murcia, Murcia 30.071, Spain.
authors.forename: A M
authors.initials: AM
authors.lastname: Somoza