Two-dimensional monomer-dimer systems are computationally intractable
- Mark Jerrum
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The classic problem of counting monomer-dimer arrangements on a two-dimensional lattice is analyzed using techniques from theoretical computer science. Under a certain assumption, made precise in the text, it can be shown that the general problem is computationally intractable. This negative result contrasts with the special case of a system with monomer density zero, for which efficient solutions have been known for some time. A second, much easier result, obtained under the same assumption, is that the partition function of a three-dimensional Ising system is computationally intractable. Again, the negative result contrasts with known efficient techniques for evaluating the partition function of a two-dimensional system.
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- Two-dimensional monomer-dimer systems are computationally intractable
Journal of Statistical Physics
Volume 48, Issue 1-2 , pp 121-134
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- Computational complexity
- Ising model
- monomer-dimer system
- Industry Sectors
- Mark Jerrum (1)
- Author Affiliations
- 1. Department of Computer Science, University of Edinburgh, EH9 3JZ, Edinburgh, Scotland