Order Parameter, Phase Transition, and Free Energies

2022 ◽  
pp. 29-43
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Free Energies

scholarly journals The improved Ginzburg-Landau technique

2018 ◽  
Vol 192 ◽  
pp. 00021
Author(s):  
Massimo Mannarelli
Keyword(s):  
Phase Transition ◽  
High Frequency ◽  
Order Parameter ◽  
Moving Average ◽  
Free Energies ◽  
Ginzburg Landau ◽  
Long Wavelength ◽  
Innovative Method ◽  
High Frequency Modes

We discuss an innovative method for the description of inhomogeneous phases designed to improve the standard Ginzburg-Landau expansion. The method is characterized by two key ingredients. The first one is a moving average of the order parameter designed to account for the long-wavelength modulations of the condensate. The second one is a sum of the high frequency modes, to improve the description of the phase transition to the restored phase. The method is applied to compare the free energies of 1D and 2D inhomogeneous structures arising in the chirally symmetric broken phase.

The flattening phase transition in systems of trapped ions

2009 ◽  
Vol 87 (10) ◽  
pp. 1425-1435 ◽  
Author(s):  
Taunia L. L. Closson ◽  
Marc R. Roussel
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Ion Trap ◽  
Anisotropy Parameter ◽  
Critical Value ◽  
Trapped Ions ◽  
Dimensional Structure ◽  
Flattening Process ◽  
Second Order Phase Transition

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x–y plane to the amplitudes along the z axis during the flattening process.

Phase transition, order parameter, and their manifestation in optical spectra of Hg2Cl2

2012 ◽  
Vol 54 (6) ◽  
pp. 1212-1219
Author(s):  
Yu. F. Markov ◽  
E. M. Roginskii ◽  
A. S. Yurkov
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Optical Spectra

Parameterization of the coupling between strain and order parameter for LuF[SeO3]

2014 ◽  
Vol 47 (2) ◽  
pp. 701-711 ◽  
Author(s):  
Oxana V. Magdysyuk ◽  
Melanie Müller ◽  
Robert E. Dinnebier ◽  
Christian Lipp ◽  
Thomas Schleid
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Structural Phase ◽  
High Temperature Phase ◽  
Temperature Phase ◽  
Time Resolved ◽  
Synchrotron Powder Diffraction ◽  
First Order Phase Transition ◽  
Temperature Phase Transition ◽  
First Order Phase

The high-temperature phase transition of LuF[SeO3] has been characterized by time-resolved high-resolution synchrotron powder diffraction. On heating, a second-order structural phase transition was found at 393 K, while on cooling the same phase transition occurs at 371 K, showing a large hysteresis typical for a first-order phase transition. Detailed analysis using sequential and parametric whole powder pattern fitting revealed that the coupling between the strain and the displacive order parameter determines the behaviour of the material during the phase transition. Different possible coupling mechanisms have been evaluated and the most probable rationalized.

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