Macroscopic Loops in the Bose Gas, Spin O(N) and Related Models

We consider a general system of interacting random loops which includes several models of interest, such as the Spin O(N) model, random lattice permutations , a version of the interacting Bose gas in discrete space and of the loop O(N) model. We consider the system in Z d , d ≥ 3 , and prove the occ...

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Bibliographic Details
Published in:Communications in mathematical physics 2023-06, Vol.400 (3), p.2081-2136
Main Authors: Quitmann, Alexandra, Taggi, Lorenzo
Format: Article
Language:English
Subjects:
Apexes
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Permutations
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:We consider a general system of interacting random loops which includes several models of interest, such as the Spin O(N) model, random lattice permutations , a version of the interacting Bose gas in discrete space and of the loop O(N) model. We consider the system in Z d , d ≥ 3 , and prove the occurrence of macroscopic loops whose length is proportional to the volume of the system. More precisely, we approximate Z d by finite boxes and, given any two vertices whose distance is proportional to the diameter of the box, we prove that the probability of observing a loop visiting both is uniformly positive. Our results hold under general assumptions on the interaction potential, which may have bounded or unbounded support or introduce hard-core constraints.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-023-04633-9