Quantum spins and random loops on the complete graph

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.

arXiv comment31 pages

References in corpus (6)

• Geometric Aspects of Quantum Spin States
• Length Distributions in Loop Soups
• Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
• The probability of long cycles in interchange processes
• The free energy in a class of quantum spin systems and interchange processes
• A numerical study of the 3D random interchange and random loop models

Cited by in corpus (5)

• Quantum group deformation of the Kittel--Shore model
• Phase Transitions, Spontaneous Symmetry Breaking, and Goldstone's Theorem
• Characterising random partitions by random colouring
• On a class of orthogonal-invariant quantum spin systems on the complete graph
• The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems