Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions
arXiv:1002.3761 · doi:10.1007/s10955-011-0292-x
Abstract
We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the special boundary conditions that are obtained from an m x n grid with free boundary conditions by adjoining one new vertex adjacent to all the sites in the leftmost column and a second new vertex adjacent to all the sites in the rightmost column. We provide numerical evidence that the partition-function zeros are becoming dense everywhere in the complex q-plane outside the limiting curve B_\infty(sq) for this model with ordinary (e.g. free or cylindrical) boundary conditions. Despite this, the infinite-volume free energy is perfectly analytic in this region.
114 pages (LaTeX2e). Includes tex file, three sty files, and 23 Postscript figures. Also included are Mathematica files data_Eq.m, data_Neq.m,and data_Diff.m. Many changes from version 1, including several proofs of previously conjectured results. Final version to be published in J. Stat. Phys
References in corpus (5)
Cited by in corpus (8)
- Partial long-range order in antiferromagnetic Potts models
- Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices
- Is the five-flow conjecture almost false?
- Phase diagram of the triangular-lattice Potts antiferromagnet
- A generalized Beraha conjecture for non-planar graphs
- The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
- Parallel family trees for transfer matrices in the Potts model
- Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions