Weak First Order Phase Transitions in Quantum Ferroelectrics

We discuss the possibility of weak first order transition in the domain of pressure induced phase transitions in a quantum ferroelectric as a consequence of order parameter fluctuations. We start with a semi-microscopic Hamiltonian, where polarization fluctuations are controlled by hydrostatic pressure via strain coupling, which above certain strength of coupling constant, kills second order transition. Using a parquet diagrammatic method, a method which retains the leading fluctuation effects in four point vertex functions, we write the free energy of the system. This fluctuation renormalized free energy is used to discuss the possibility of first order transition at zero temperature and at finite temperature as well. Asymptotic analysis of fluctuation corrected vertices, in a short range model, predicts small but finite jump in the order parameter near the mean field quantum critical point at zero temperature. In case of finite temperature transition near quantum critical point such a possibility is found to be extremely weak. The formalism is quite general and is applicable to certain class of systems undergoing quantum phase transition and the results are interesting in context of some experimental findings on quantum paraelectrics like SrTiO3 and KTaO3. PACS numbers: 77.80.Bh, 64.70.Tg Weak First Order Phase Transitions in Quantum Ferroelectrics 2