  We study the small-world network model, which mimics the transition between
regular-lattice and random-lattice behavior in social networks of increasing
size. We contend that the model displays a normal continuous phase transition
with a divergent correlation length as the degree of randomness tends to zero.
We propose a real-space renormalization group transformation for the model and
demonstrate that the transformation is exact in the limit of large system size.
We use this result to calculate the exact value of the single critical exponent
for the system, and to derive the scaling form for the average number of
"degrees of separation" between two nodes on the network as a function of the
three independent variables. We confirm our results by extensive numerical
simulation.
