Chromatic polynomials of large triangular lattices
- 21 October 1987
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 20 (15) , 5241-5261
- https://doi.org/10.1088/0305-4470/20/15/037
Abstract
Evaluating the q colourings of a lattice is equivalent to solving the q-state zero-temperature antiferromagnetic Potts model. This has recently been done exactly for an infinite triangular lattice with q real. Here the results are extended to the full complex q plane, giving the limiting distribution of the zeros of the chromatic polynomial. The results are compared with finite lattice calculations and the occurrence of isolated real zeros converging on the Beraha numbers is noted.Keywords
This publication has 32 references indexed in Scilit:
- q colourings of the triangular latticeJournal of Physics A: General Physics, 1986
- Limits of chromatic zeros of some families of mapsJournal of Combinatorial Theory, Series B, 1980
- Series expansions from corner transfer matrices: The square lattice Ising modelJournal of Statistical Physics, 1979
- Is the four-color conjecture almost false?Journal of Combinatorial Theory, Series B, 1979
- Mathematical GamesScientific American, 1976
- Equivalence of the Potts model or Whitney polynomial with an ice-type modelJournal of Physics A: General Physics, 1976
- Approximations for chromatic polynomialsJournal of Combinatorial Theory, Series B, 1976
- Recursive families of graphsJournal of Combinatorial Theory, Series B, 1972
- On the random-cluster modelPhysica, 1972
- Theorems on the Partition Functions of the Heisenberg FerromagnetsJournal of the Physics Society Japan, 1970