A note on the monomer-dimer model
Authors
- Quitmann, Alexandra
ORCID: 0000-0003-4898-1963
2020 Mathematics Subject Classification
- 60K35 82B20
Keywords
- Monomer-dimer model, statistical mechanics
DOI
Abstract
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 truncated spin-spin correlations in classical spin systems. Our proof is based on the cluster expansion technique.
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