Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical two-point functions for long-range statistical-mechanical
  models in high dimensions   We consider long-range self-avoiding walk, percolation and the Ising model on
$\mathbb{Z}^d$ that are defined by power-law decaying pair potentials of the
form $D(x)\asymp|x|^{-d-\alpha}$ with $\alpha>0$. The upper-critical dimension
$d_{\mathrm{c}}$ is $2(\alpha\wedge2)$ for self-avoiding walk and the Ising
model, and $3(\alpha\wedge2)$ for percolation. Let $\alpha\ne2$ and assume
certain heat-kernel bounds on the $n$-step distribution of the underlying
random walk. We prove that, for $d>d_{\mathrm{c}}$ (and the spread-out
parameter sufficiently large), the critical two-point function
$G_{p_{\mathrm{c}}}(x)$ for each model is asymptotically
$C|x|^{\alpha\wedge2-d}$, where the constant $C\in(0,\infty)$ is expressed in
terms of the model-dependent lace-expansion coefficients and exhibits crossover
between $\alpha<2$ and $\alpha>2$. We also provide a class of random walks that
satisfy those heat-kernel bounds.

33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
19
The categories of this paper are: eess
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs