Quantum spins and random loops on the complete graph
Mathematical Physics
2021-06-30 v2 math.MP
Probability
Abstract
We present a systematic analysis of quantum Heisenberg-, XY- and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which we study by calculating the generating function of expectations of powers of the averaged spin density. Various critical exponents are determined. Certain objects of the associated loop models are shown to have properties of Poisson--Dirichlet distributions.
Cite
@article{arxiv.1811.12834,
title = {Quantum spins and random loops on the complete graph},
author = {Jakob E. Björnberg and Jürg Fröhlich and Daniel Ueltschi},
journal= {arXiv preprint arXiv:1811.12834},
year = {2021}
}
Comments
31 pages