# Universal behaviour of 3D loop soup models

@article{Ueltschi2017UniversalBO,
title={Universal behaviour of 3D loop soup models},
author={Daniel Ueltschi},
journal={arXiv: Statistical Mechanics},
year={2017}
}
• Daniel Ueltschi
• Published 2017
• Physics, Mathematics
• arXiv: Statistical Mechanics
• These notes describe several loop soup models and their {\it universal behaviour} in dimensions greater or equal to 3. These loop models represent certain classical or quantum statistical mechanical systems. These systems undergo phase transitions that are characterised by changes in the structures of the loops. Namely, long-range order is equivalent to the occurrence of macroscopic loops. There are many such loops, and the joint distribution of their lengths is always given by a {\it Poisson… CONTINUE READING

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 44 REFERENCES

## Length distributions in loop soups.

• Medicine, Physics
• Physical review letters
• 2013
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Random loop representations for quantum spin systems

VIEW 3 EXCERPTS

## Quantum Heisenberg models and their probabilistic representations

• Mathematics, Physics
• 2011
VIEW 3 EXCERPTS

## Infrared bounds, phase transitions and continuous symmetry breaking

• Mathematics
• 1976

## Geometric aspects of quantum spin states

• Mathematics, Physics
• 1994
VIEW 2 EXCERPTS

## ATOMIC THEORY OF THE /lambda/ TRANSITION IN HELIUM

VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

## A numerical study of the 3D random interchange and random loop models

• Physics, Mathematics
• 2015

## Random fragmentation and coagulation processes

VIEW 3 EXCERPTS

## Percolation transition in the Bose gas: II

VIEW 2 EXCERPTS

## Lattice Permutations and Poisson-Dirichlet Distribution of Cycle Lengths

• Physics, Mathematics
• 2012
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL