Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-field behavior for long- and finite range Ising model, percolation
  and self-avoiding walk   We consider self-avoiding walk, percolation and the Ising model with long and
finite range. By means of the lace expansion we prove mean-field behavior for
these models if $d>2(\alpha\wedge2)$ for self-avoiding walk and the Ising
model, and $d>3(\alpha\wedge2)$ for percolation, where $d$ denotes the
dimension and $\alpha$ the power-law decay exponent of the coupling function.
We provide a simplified analysis of the lace expansion based on the
trigonometric approach in Borgs et al. (2007)

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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
16
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: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an