scholarly journals The Free Energy of the Potts Model: From the Continuous to the First-Order Transition Region

1993 ◽  
Vol 23 (8) ◽  
pp. 547-552 ◽  
Author(s):  
T Bhattacharya ◽  
R Lacaze ◽  
A Morel
Keyword(s):  
Free Energy ◽  
Transition Region ◽  
Potts Model ◽  
Order Transition ◽  
First Order ◽  
First Order Transition

scholarly journals EFFECTS OF STRAIN COUPLING AND MARGINAL DIMENSIONALITY IN THE NATURE OF PHASE TRANSITION IN QUANTUM PARAELECTRICS

2013 ◽  
Vol 27 (08) ◽  
pp. 1350028 ◽  
Author(s):  
NABYENDU DAS
Keyword(s):  
Free Energy ◽  
Critical Point ◽  
Finite Temperature ◽  
Order Parameter ◽  
Quantum Critical Point ◽  
Order Transition ◽  
Zero Temperature ◽  
First Order ◽  
Quantum Paraelectrics ◽  
First Order Transition

Here a recently observed weak first order transition in doped SrTiO 3 [Taniguchi, Itoh and Yagi, Phys. Rev. Lett.99, 017602 (2007)] is argued to be a consequence of the coupling between strain and order parameter fluctuations. Starting with a semi-microscopic action, and using renormalization group equations for vertices, we write the free energy of such a system. This fluctuation renormalized 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 predicts small but a finite discontinuity in the order parameter near a 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. Results are in accord with some experimental findings on quantum paraelectrics such as SrTiO 3 and KTaO 3.

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