Coexistence, enhancements and short loops in random walk loop soups

Forien, Nicolas; Quattropani, Matteo; Quitmann, Alexandra; Taggi, Lorenzo

doi:10.2140/pmp.2024.5.753

Prob. Math. Phys.

2024

DOI: 10.2140/pmp.2024.5.753

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Coexistence, enhancements and short loops in random walk loop soups

Nicolas Forien,

Matteo Quattropani,

Alexandra Quitmann

et al.

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2024

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Decay of correlations in the monomer-dimer model

Quitmann

2024

Journal of Mathematical Physics

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We consider the monomer-dimer model, whose realisations are spanning sub-graphs of a given graph such that every vertex has degree zero or one. The measure depends on a parameter, the monomer activity, which rewards the total number of monomers. We consider general correlation functions including monomer-monomer correlations and dimer-dimer covariances. We show that these correlations decay exponentially fast with the distance if the monomer activity is strictly positive. Our result improves a previous upper bound from van den Berg and is of interest due to its relation to transverse spin-spin correlations in classical spin systems. Our proof is based on the cluster expansion technique.

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Decay of correlations in the monomer-dimer model

Quitmann

2024

Journal of Mathematical Physics

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Coexistence, enhancements and short loops in random walk loop soups

Cited by 1 publication

References 32 publications

Decay of correlations in the monomer-dimer model

Decay of correlations in the monomer-dimer model

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