Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation algorithms for two-state anti-ferromagnetic spin systems
  on bounded degree graphs   In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial
approximation scheme for count- ing exponentially weighted independent sets
(equivalently, approximating the partition function of the hard-core model from
statistical physics) on graphs of degree at most d, up to the critical activity
for the uniqueness of the Gibbs measure on the infinite d-regular tree. More
recently Sly (Sly, 2010) showed that this is optimal in the sense that if there
is an FPRAS for the hard-core partition function on graphs of maximum degree d
for activities larger than the critical activity on the infinite d-regular tree
then NP = RP. In this paper, we extend Weitz's approach to derive a
deterministic fully polynomial approx- imation scheme for the partition
function of the anti-ferromagnetic Ising model with arbitrary field on graphs
of maximum degree d, up to the corresponding critical point on the d-regular
tree. The main ingredient of our result is a proof that for two-state
anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing
implies strong spatial mixing. This in turn uses a message-decay argument which
extends a similar approach proposed recently for the hard-core model by
Restrepo et al (Restrepo et al, 2011) to the case of the anti-ferromagnetic
Ising model with arbitrary field. By a standard correspondence, these results
translate to arbitrary two-state anti-ferromagnetic spin systems with soft
constraints.

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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol