Exact asymptotics of monomer-dimer model on rectangular semi-infinite lattices
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2006
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| _version_ | 1866917655828496384 |
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| author | Kong, Yong |
| author_facet | Kong, Yong |
| contents | By using the asymptotic theory of Pemantle and Wilson, exact asymptotic expansions of the free energy of the monomer-dimer model on rectangular $n \times \infty$ lattices in terms of dimer density are obtained for small values of $n$, at both high and low dimer density limits. In the high dimer density limit, the theoretical results confirm the dependence of the free energy on the parity of $n$, a result obtained previously by computational methods. In the low dimer density limit, the free energy on a cylinder $n \times \infty$ lattice strip has exactly the same first $n$ terms in the series expansion as that of infinite $\infty \times \infty$ lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_cond_mat_0611449 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | Exact asymptotics of monomer-dimer model on rectangular semi-infinite lattices Kong, Yong Statistical Mechanics By using the asymptotic theory of Pemantle and Wilson, exact asymptotic expansions of the free energy of the monomer-dimer model on rectangular $n \times \infty$ lattices in terms of dimer density are obtained for small values of $n$, at both high and low dimer density limits. In the high dimer density limit, the theoretical results confirm the dependence of the free energy on the parity of $n$, a result obtained previously by computational methods. In the low dimer density limit, the free energy on a cylinder $n \times \infty$ lattice strip has exactly the same first $n$ terms in the series expansion as that of infinite $\infty \times \infty$ lattice. |
| title | Exact asymptotics of monomer-dimer model on rectangular semi-infinite lattices |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/cond-mat/0611449 |