Two-dimensional monomer-dimer systems are computationally intractable
Abstract
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.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- July 1987
- DOI:
- 10.1007/BF01010403
- Bibcode:
- 1987JSP....48..121J