Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-05-17
Physics
Condensed Matter
Statistical Mechanics
Minor corrections in text, Fig. 3 replaced
Scientific paper
10.1088/0305-4470/34/38/303
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.
Chakrabarti Bikas K.
Sen Parongama
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