Phase diagram of UGe2. Whether there are quantum phase transitions ?

The phase diagram of several itinerant ferromagnets reveals the common feature. The phase transition temperature decreases with pressure increase and reaches zero value at some critical pressure $P_c$ such that at low enough temperatures one can expect critical behavior specific for quantum phase transition. It is not the case, however. Being the second order at ambient pressure the transition from paramagnetic to ferromagnetic state at high pressures - low temperatures is transformed to the discontinuous jump. We discuss the magneto-elastic mechanism of development of the first order type instability at the phase transition to the ferromagnet state in strongly anisotropic ferromagnet UGe2. Using the parameters characterizing the properties of UGe$_2$ we argue the effectiveness of this mechanism transforming the very weak first order type transition to the really observable one.