Quantum first order phase transitions
  The scaling theory of critical phenomena has been successfully extended for classical first order transitions even though the correlation length does not diverge in these transitions. In this paper we apply the scaling ideas to quantum first order transitions. The usefulness of this approach is illustrated treating the problems of a superconductor coupled to a gauge field and of a biquadratic Heisenberg chain, at zero temperature. In both cases there is a latent energy associated with their discontinuous quantum transitions. We discuss the effects of disorder and give a general criterion for it's relevance in these transitions. 
Mucio A. Continentino and Andre S. Ferreira