Finite-size scaling at the first-order quantum transitions of quantum   Potts chains
  We investigate finite-size effects in quantum systems at first-order quantum transitions. For this purpose we consider the one-dimensional q-state Potts models which undergo a first-order quantum transition for any q>4, separating the quantum disordered and ordered phases with a discontinuity in the energy density of the ground state. The low-energy properties around the transition show finite-size scaling, described by general scaling ansatzes with respect to appropriate scaling variables. The size dependence of the scaling variables presents a particular sensitiveness to boundary conditions, which may be considered as a peculiar feature of first-order quantum transitions. 
Massimo Campostrini, Jacopo Nespolo, Andrea Pelissetto, and Ettore   Vicari
cond-mat.stat-mech hep-lat