Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating Pairwise Correlations in the Ising Model   In the Ising model, we consider the problem of estimating the covariance of
the spins at two specified vertices. In the ferromagnetic case, it is easy to
obtain an additive approximation to this covariance by repeatedly sampling from
the relevant Gibbs distribution. However, we desire a multiplicative
approximation, and it is not clear how to achieve this by sampling, given that
the covariance can be exponentially small. Our main contribution is a fully
polynomial time randomised approximation scheme (FPRAS) for the covariance. We
also show that that the restriction to the ferromagnetic case is essential ---
there is no FPRAS for multiplicatively estimating the covariance of an
antiferromagnetic Ising model unless RP = #P. In fact, we show that even
determining the sign of the covariance is #P-hard in the antiferromagnetic
case.

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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th