Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of Convergence for the Lattice Monomer-Dimer Cluster Expansion I,
  a Simplified Model   We present some promising ideas to treat the problem of making completely
rigorous the development of our expression for $\lambda_d(p)$ of the
monomer-dimer problem on a $d$-dimensional hypercubic lattice
\begin{equation}\label{abstract1}
  \lambda_d(p)=\frac{1}{2}\Big(p\ln(2d)-p\ln(p)-2(1-p)\ln(1-p)-p\Big)
  +\sum_{k=2}a_k(d)p^k \end{equation} where $a_k(d)$ is a sum of powers
$(1/d)^r$ for \begin{equation}\label{abstract2}
  k-1\leq r\leq k/2 \end{equation} In fact as we will point out one has
allready rigorously established the convergence of the sum in expression for
$\lambda$ for small $p$. It is the $d$ dependence of $a_k(d)$ that has yet to
be rigorously shown. We do not now know how to complete the proof.

34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph