Self-consistent treatment of a phase transition in a system with a vector order parameter

1974 ◽  
Vol 10 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Marco Zannetti
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Self Consistent ◽  
Consistent Treatment

Self-consistent treatment of a phase transition

1973 ◽  
Vol 9 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Daniel J. Amit ◽  
Marco Zannetti
Keyword(s):  
Phase Transition ◽  
Self Consistent ◽  
Consistent Treatment

scholarly journals An Improved Equation of State for Hydrogen

1993 ◽  
Vol 137 ◽  
pp. 307-309 ◽  
Author(s):  
D. Saumon ◽  
G. Chabrier
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Order Phase Transition ◽  
Equations Of State ◽  
First Order ◽  
First Order Phase Transition ◽  
Self Consistent ◽  
Plasma Phase ◽  
Consistent Treatment ◽  
First Order Phase

An improved theory of fluid hydrogen at high density, based on a detailed treatment of inter-particle correlations and a self-consistent treatment of pressure ionization, has become available recently (Chabrier 1990, Saumon and Chabrier 1991, 1992). We present a preliminary comparison between this new EOS (hereatfer SC) and equations of state frequently used in astrophysical contexts, namely: Fontaine, Graboske and Van Horn 1977 (FGVH), Däppen et al. 1988 (MHD) and Magni and Mazzitelli 1979 (MM).The SC theory predicts a first-order phase transition in the region of pressure-ionization (the so-called Plasma Phase Transition, or PPT), between an essentially neutral mixture of atoms and molecules (xe– < 10−2), and a partially ionized plasma (xe– ≈ 50 %), with a critical point located at Pc = 0.614 Mbar, Tc = 15300K and pc = 0.35 g/cm3.

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.

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