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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.13632 |
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| _version_ | 1866914970862616576 |
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| author | Quitmann, Alexandra |
| author_facet | Quitmann, Alexandra |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13632 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Decay of correlations in the monomer-dimer model Quitmann, Alexandra Probability 60K35, 82B20 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. |
| title | Decay of correlations in the monomer-dimer model |
| topic | Probability 60K35, 82B20 |
| url | https://arxiv.org/abs/2309.13632 |