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|Title:||Packing dimers on (2p+1) × (2q+1) lattices|
|Citation:||Kong, Y. (2006-01). Packing dimers on (2p+1) × (2q+1) lattices. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 73 (1) : -. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevE.73.016106|
|Abstract:||We use computational method to investigate the number of ways to pack dimers on m×n lattices, where both m and n are odd. In this case, there is always a single vacancy in the lattices. We show that the dimer configuration numbers on (2k+1) × (2k+1) odd square lattices have some remarkable number-theoretical properties in parallel to those of close-packed dimers on 2k×2k even square lattices, for which an exact solution exists. Furthermore, we demonstrate that there is an unambiguous logarithmic term in the finite size correction of free energy of odd-by-odd lattice strips with any width n≥1. This logarithmic term determines the distinct behavior of the free energy of odd square lattices. These findings reveal a deep and previously unexplored connection between statistical physics models and number theory and indicate the possibility that the monomer-dimer problem might be solvable. © 2006 The American Physical Society.|
|Source Title:||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Appears in Collections:||Staff Publications|
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