Macroscopic cycles for the interchange and quantum Heisenberg models on random regular graphs

2022/09/27 by Rémy Poudevigne, Poudevigne, Rémy
Mathematics · Physics and Astronomy · #60J27 #60K35 #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2209.13370

openalex publication_date 2022/09/27 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

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.

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