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Spatial random permutations and infinite cycles

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arxiv 0711.1188 v2 pith:PVPM4UUD submitted 2007-11-08 math-ph math.MP

Volker Betz , Daniel Ueltschi This is my paper · ORCID
classification math-phmath.MP
keywords permutationsspatialcyclesinfiniterandomaccordingboseconsider
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We consider systems of spatial random permutations, where permutations are weighed according to the point locations. Infinite cycles are present at high densities. The critical density is given by an exact expression. We discuss the relation between the model of spatial permutations and the ideal and interacting quantum Bose gas.

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  1. On the Ising Phase Transition in the Infrared-Divergent Spin Boson Model

    math-ph 2025-01 conditional novelty 8.0 of 10

    Infrared-divergent spin boson model loses its ground state above a finite critical coupling, proved via long range order in a dual continuum Ising model.

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