2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158100We 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.11 pages, 14 figures. Statements made clearer. Corrected an error in the (present) Eq. 61. Figs. 1 and 2 and 9-12 changed. Added two Figs. related to the phase diagramDisordered Systems and Neural NetworksStatistical Mechanicstext