Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small-world phenomena and the statistics of linear polymer networks   A regular lattice in which the sites can have long range connections at a
distance l with a probabilty $P(l) \sim l^{-\delta}$, in addition to the short
range nearest neighbour connections, shows small-world behaviour for $0 \le
\delta < \delta_c$. In the most appropriate physical example of such a system,
namely the linear polymer network, the exponent $\delta$ is related to the
exponents of the corresponding n-vector model in the $n \to 0$ limit, and its
value is less than $\delta_c$. Still, the polymer networks do not show
small-world behaviour. Here, we show that this is due a (small value)
constraint on the number q of long range connections per monomer in the
network. In the general $\delta - q$ space, we obtain a phase boundary
separating regions with and without small-world behaviour, and show that the
polymer network falls marginally in the regular lattice region.

15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin