Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical two-point function for long-range models with power-law
  couplings: The marginal case for $d\ge d_c$   Consider the long-range models on $\mathbb{Z}^d$ of random walk,
self-avoiding walk, percolation and the Ising model, whose
translation-invariant 1-step distribution/coupling coefficient decays as
$|x|^{-d-\alpha}$ for some $\alpha>0$. In the previous work (Ann. Probab., 43,
639--681, 2015), we have shown in a unified fashion for all $\alpha\ne2$ that,
assuming a bound on the "derivative" of the $n$-step distribution (the
compound-zeta distribution satisfies this assumed bound), the critical
two-point function $G_{p_c}(x)$ decays as $|x|^{\alpha\wedge2-d}$ above the
upper-critical dimension $d_c\equiv(\alpha\wedge2)m$, where $m=2$ for
self-avoiding walk and the Ising model and $m=3$ for percolation.
  In this paper, we show in a much simpler way, without assuming a bound on the
derivative of the $n$-step distribution, that $G_{p_c}(x)$ for the marginal
case $\alpha=2$ decays as $|x|^{2-d}/\log|x|$ whenever $d\ge d_c$ (with a large
spread-out parameter $L$). This solves the conjecture in the previous work,
extended all the way down to $d=d_c$, and confirms a part of predictions in
physics (Brezin, Parisi, Ricci-Tersenghi, J. Stat. Phys., 157, 855--868, 2014).
The proof is based on the lace expansion and new convolution bounds on power
functions with log corrections.

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th