  We apply a novel method (presented in part I) to solve several small-world
models for which the method can be applied analytically: the Viana-Bray model
(which can be seen as a 0 or infinite dimensional small-world model), the
one-dimensional chain small-world model, and the small-world spherical model in
generic dimension. In particular, we analyze in detail the one-dimensional
chain small-world model with negative short-range coupling showing that in this
case, besides a second-order spin glass phase transition, there are two
critical temperatures corresponding to first- or second-order phase
transitions.
