  While network abrupt breakdowns due to overloads and cascading failures have
been studied extensively, the critical exponents and the universality class of
such phase transitions have not been discussed. Here, we study breakdowns
triggered by failures of links and overloads in networks with a spatial
characteristic link length $\zeta$. Our results indicate that this abrupt
transition has features and critical exponents similar to those of
interdependent networks, suggesting that both systems are in the same
universality class. For weakly embedded systems (i.e., $\zeta$ of the order of
the system size $L$) we observe a mixed-order transition, where the order
parameter collapses following a long critical plateau. On the other hand,
strongly embedded systems (i.e., $\zeta \ll L$) exhibit a pure first-order
transition, involving nucleation and the growth of damage. The system's
critical behavior in both limits is similar to that observed in interdependent
networks.
