  Quantum phase transitions have been the subject of intense investigations in
the last two decades [1]. Among other problems, these phase transitions are
relevant in the study of heavy fermion systems, high temperature
superconductors and Bose-Einstein condensates. More recently there is
increasing evidence that in many systems which are close to a quantum critical
point (QCP) different phases are in competition. In this paper we show that the
main effect of this competition is to give rise to inhomogeneous behavior
associated with quantum first order transitions. These effects are described
theoretically using an action that takes into account the competition between
different order parameters. The method of the effective potential is used to
calculate the quantum corrections to the classical functional. These
corrections generally change the nature of the QCP and give rise to interesting
effects even in the presence of non-critical fluctuations. An unexpected result
is the appearance of an inhomogeneous phase with two values of the order
parameter separated by a first order transition. Finally, we discuss the
universal behavior of systems with a weak first order zero temperature
transition in particular as the transition point is approached from finite
temperatures. The thermodynamic behavior along this line is obtained and shown
to present universal features.
