Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds and Series for the Ground State Entropy of the Potts
  Antiferromagnet on Archimedean Lattices and their Duals   We prove a general rigorous lower bound for
$W(\Lambda,q)=\exp(S_0(\Lambda,q)/k_B)$, the exponent of the ground state
entropy of the $q$-state Potts antiferromagnet, on an arbitrary Archimedean
lattice $\Lambda$. We calculate large-$q$ series expansions for the exact
$W_r(\Lambda,q)=q^{-1}W(\Lambda,q)$ and compare these with our lower bounds on
this function on the various Archimedean lattices. It is shown that the lower
bounds coincide with a number of terms in the large-$q$ expansions and hence
serve not just as bounds but also as very good approximations to the respective
exact functions $W_r(\Lambda,q)$ for large $q$ on the various lattices
$\Lambda$. Plots of $W_r(\Lambda,q)$ are given, and the general dependence on
lattice coordination number is noted. Lower bounds and series are also
presented for the duals of Archimedean lattices. As part of the study, the
chromatic number is determined for all Archimedean lattices and their duals.
Finally, we report calculations of chromatic zeros for several lattices; these
provide further support for our earlier conjecture that a sufficient condition
for $W_r(\Lambda,q)$ to be analytic at $1/q=0$ is that $\Lambda$ is a regular
lattice.

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The categories of this paper are: q-alg
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th