3,967 research outputs found
End Graph Effects on Chromatic Polynomials for Strip Graphs of Lattices and their Asymptotic Limits
We report exact calculations of the ground state degeneracy per site
(exponent of the ground state entropy) of the -state Potts
antiferromagnet on infinitely long strips with specified end graphs for free
boundary conditions in the longitudinal direction and free and periodic
boundary conditions in the transverse direction. This is equivalent to
calculating the chromatic polynomials and their asymptotic limits for these
graphs. Making the generalization from to , we determine the full locus on which is nonanalytic in the
complex plane. We report the first example for this class of strip graphs
in which encloses regions even for planar end graphs. The bulk of
the specific strip graph that exhibits this property is a part of the Archimedean lattice.Comment: 27 pages, Revtex, 11 encapsulated postscript figures, Physica A, in
pres
Dense packing on uniform lattices
We study the Hard Core Model on the graphs
obtained from Archimedean tilings i.e. configurations in with the nearest neighbor 1's forbidden. Our
particular aim in choosing these graphs is to obtain insight to the geometry of
the densest packings in a uniform discrete set-up. We establish density bounds,
optimal configurations reaching them in all cases, and introduce a
probabilistic cellular automaton that generates the legal configurations. Its
rule involves a parameter which can be naturally characterized as packing
pressure. It can have a critical value but from packing point of view just as
interesting are the noncritical cases. These phenomena are related to the
exponential size of the set of densest packings and more specifically whether
these packings are maximally symmetric, simple laminated or essentially random
packings.Comment: 18 page
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