Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magnetism of Cu_6 Ge_6 O_{18}-x H_2 O (x = 0 ~ 6), a compound of the
  one-dimensional Heisenberg $S = 1/2$ model with competing antiferromagnetic
  interactions   We measured the magnetic susceptibilities of Cu$_6$Ge$_6$O$_{18}$-xH$_2$O ($x
= 0 \sim 6$). Susceptibility above the antiferromagnetic (AF) transition
temperature ($T_{\rm N}$) agrees with susceptibility of the one-dimensional
Heisenberg $S = 1/2$ model with competing AF interactions. From the estimated
ratio between nearest-neighbor and next-nearest-neighbor AF exchange
interactions, the spin system is probably located near a boundary between spin
systems with gapless and gapped magnetic excitation. The value of $T_{\rm
N}/T_{\rm max}$, where $T_{\rm max}$ is temperature at which the susceptibility
is maximum, shows a unique dependence on $x$. The $x$ dependence can be
explained qualitatively by taking phase transition as a function of $x$ and the
effect of disorder into account.

35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg