# 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} }

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

#### Citations

##### Publications citing this paper.

SHOWING 1-3 OF 3 CITATIONS

## Quantum Spins and Random Loops on the Complete Graph

VIEW 1 EXCERPT

CITES RESULTS

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 44 REFERENCES

## Length distributions in loop soups.

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Random loop representations for quantum spin systems

VIEW 3 EXCERPTS

## Geometric aspects of quantum spin states

VIEW 2 EXCERPTS

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

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## 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

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL