Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absence of gap for infinite half--integer spin ladders with an odd
  number of legs   A proof is presented for the absence of gap for spin $1/2$ ladders with an
odd number of legs, in the infinite leg length limit. This result is relevant
to the current discussion of coupled one--dimensional spin systems, a physical
realization of which are vanadyl pyrophosphate, (VO)$_2$P$_2$O$_7$, and
stoichiometric Sr$_{n-1}$ Cu$_{n+1}$ O$_{2n}$ (with $n=3,5,7,9,\dots$).

0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an