Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-06-04
Physics
Condensed Matter
Statistical Mechanics
8 pages, 4 figures
Scientific paper
Considering a recent experimental indication that certain doped dielectric materials, such as SrTiO$_3$ and KTaO$_3$, are on the verge of a first order quantum phase transition, the effects of order parameter fluctuations in those materials near such a transition are discussed. We start with a semi-microscopic action, where transverse paraelectric(or optical mode) fluctuations are controlled by hydrostatic pressure via strain coupling,which above a certain value of strength, kills the second order transition. Using self-consistent parquet re-summations, which retain the leading fluctuation effects in four point vertex function, we write the free energy of the system. This fluctuation re-normalized free energy is then used to discuss the possibility of first order transition at zero temperature as well as at finite temperature. An asymptotic analysis of fluctuation corrected vertices, with strain induced long range interaction, predicts small but a finite jump in the order parameter near the mean field quantum critical point at zero temperature. In the 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 weak quantum first order phase transition.
Das Nabyendu
Mishra Suresh G.
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