ϵ expansion for the free energy of the continuous three-state Potts model: evidence for a first-order transition

1975 ◽  
Vol 8 (7) ◽  
pp. 1125-1129 ◽  
Author(s):  
J Rudnick
Keyword(s):  
Free Energy ◽  
Potts Model ◽  
Order Transition ◽  
First Order ◽  
Model Evidence ◽  
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.

scholarly journals SUSTAINING SUPERCOOLED MIXED PHASE VIA RESONANT OSCILLATIONS OF THE ORDER PARAMETER

2004 ◽  
Vol 19 (10) ◽  
pp. 1511-1524
Author(s):  
RAJARSHI RAY ◽  
SOMA SANYAL ◽  
AJIT M. SRIVASTAVA
Keyword(s):  
Free Energy ◽  
Order Parameter ◽  
Condensed Matter ◽  
Mixed Phase ◽  
Order Transition ◽  
Stable Phase ◽  
Driving Frequency ◽  
First Order ◽  
Parameter Field ◽  
First Order Transition

We investigate the dynamics of a first order transition when the order parameter field undergoes resonant oscillations, driven by a periodically varying parameter of the free energy. This parameter could be a background oscillating field as in models of pre-heating after inflation. In the context of condensed matter systems, it could be temperature T, or pressure, external electric/magnetic field etc. We show that with suitable driving frequency and amplitude, the system remains in a type of mixed phase, without ever completing transition to the stable phase, even when the oscillating parameter of the free energy remains below the corresponding critical value (for example, with oscillating temperature, T always remains below the critical temperature Tc). This phenomenon may have important implications. In cosmology, it will imply prolonged mixed phase in a first order transition due to coupling with background oscillating fields. In condensed matter systems, it will imply that using oscillating temperature (or, more appropriately, pressure waves) one may be able to sustain liquids in a mixed phase indefinitely at low temperatures, without making transition to the frozen phase.

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