Macroscopic cycles for the interchange and quantum Heisenberg models on random regular graphs
classification
🧮 math.PR
math-phmath.MP
keywords
graphmodelgraphsheisenberginterchangequantumrandomcomplete
read the original abstract
The interchange process is a random permutation model that was introduced as a way to study the quantum Heisenberg model. For this model, progress had been made on some specific graphs: trees, the hypercube, the Hamming graph, the complete graph and the two block graph. Here we show that for large enough parameters, both the interchange process and the quantum Heisenberg model have macroscopic clusters on random d-regular graphs. Such a result was only known for the complete graph and the two blocks graph.
This paper has not been read by Pith yet.
Forward citations
Cited by 1 Pith paper
-
Macroscopic loops in the random loop model on sparse random graphs
Macroscopic loops exist in the random loop model on sparse random graphs above an explicit edge density threshold depending on loop weight θ and cross parameter u.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.