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|Title:||Asymptotics of the monomer-dimer model on two-dimensional semi-infinite lattices||Authors:||Kong, Y.||Issue Date:||30-May-2007||Citation:||Kong, Y. (2007-05-30). Asymptotics of the monomer-dimer model on two-dimensional semi-infinite lattices. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 75 (5) : -. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevE.75.051123||Abstract:||By using the asymptotic theory of Pemantle and Wilson [R. Pemantle and M. C. Wilson, J. Comb. Theory, Ser. AJCBTA70097-316510.1006/jcta.2001.3201 97, 129 (2002)], asymptotic expansions of the free energy of the monomer-dimer model on two-dimensional semi-infinite ×n 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 by Y. Kong [Y. Kong, Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.74.061102 74, 061102 (2006); Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.73.016106 73, 016106 (2006);Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.74.011102 74, 011102 (2006)]. In the low-dimer-density limit, the free energy on a cylinder ×n lattice strip has exactly the same first n terms in the series expansion as that of an infinite × lattice. © 2007 The American Physical Society.||Source Title:||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics||URI:||http://scholarbank.nus.edu.sg/handle/10635/102902||ISSN:||15393755||DOI:||10.1103/PhysRevE.75.051123|
|Appears in Collections:||Staff Publications|
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