Incompletely ordered phase in the three-dimensional six-state clock model: Evidence for an absence of ordered phases ofXYcharacter

1991 ◽  
Vol 43 (10) ◽  
pp. 8654-8657 ◽  
Author(s):  
Yohtaro Ueno ◽  
Kikuo Mitsubo
Keyword(s):  
Three Dimensional ◽  
Clock Model ◽  
Ordered Phases ◽  
Model Evidence

scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

A Shift-Lattice Interpretation of Structures in the Au4Mn Region of the Au-Mn System

1996 ◽  
Vol 49 (8) ◽  
pp. 873
Author(s):  
RJD Tilley ◽  
RP Williams
Keyword(s):  
Three Dimensional ◽  
One Dimensional ◽  
Ordered Phases ◽  
The Matrix ◽  
Unit Cells ◽  
The Face ◽  
Cubic Structure ◽  
Diffraction Patterns

The structures of a number of ordered phases in the Au-Mn system derived from the face- centred cubic structure of Au4Mn have been described in a systematic manner by use of shift-lattice distributions of the manganese atoms throughout the matrix of the alloys. The simplest structures are describable in terms of one-dimensional shift lattices, but many are best treated as two- or three-dimensional shift lattices. This approach has allowed structural correlations to be presented that have not been described previously and the variation in stoichiometry of these phases to be accounted for without recourse to defect populations. The diffraction patterns of such structures are also discussed, especially incommensurate patterns from materials with 'infinitely large' crystallographic unit cells.

scholarly journals Three-dimensional structure of the ordered phases of Hg on Cu(001)

1992 ◽  
Vol 45 (7) ◽  
pp. 3708-3717 ◽  
Author(s):  
Wei Li ◽  
Jingsu Lin ◽  
M. Karimi ◽  
P. A. Dowben ◽  
G. Vidali
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Three Dimensional Structure ◽  
Ordered Phases

On the praseodymium + oxygen system

1966 ◽  
Vol 259 (1106) ◽  
pp. 583-614 ◽  
Keyword(s):  
Composition Range ◽  
Three Dimensional ◽  
Cubic Phase ◽  
Ambient Conditions ◽  
Praseodymium Oxide ◽  
Narrow Homogeneity Range ◽  
Plausible Model ◽  
Wide Range ◽  
Ordered Phases ◽  
Miscibility Gaps

An isobaric survey of the system praseodymium oxide + oxygen has been made at oxygen pressures between 0 and 1 atm and in the temperature range 200 to 1150 °C. The derived isobaric sections enable a three-dimensional phase diagram (pressure, temperature, composition) to be constructed with considerable certainty and detail for the composition range PrOj.gg to PrOj.g*. Reasonable extensions to cover the complete range between the sesquioxide and dioxide are proposed, and a projection of the diagram on to the temperature-composition plane is presented. At lower temperatures several discrete, ordered phases of narrow homogeneity range exist. These constitute an homologous series P r„02n_2, with n = 4, 7, 9 ,1 0 ,1 1 ,1 2 , oo. At higher temperatures two wide-range solid solutions obtain: <r, a body-centred cubic phase with a maximum composition range ca. PrOj.gQ to PrOj.yo; and a, a face-centred cubic phase of composition P r O ^ to P r 0 2. The fields of stability of the various phases are defined and the ambient conditions at many invariant axes (peritectoid and eutectoid) enumerated. Miscibility gaps with upper consolute points are exceptional; order-disorder peritectoid transformations are common. Hysteresis in phase transformations is confirmed, and the results further demonstrate the existence of metastable states in phase reactions involving an increase in structural order. The appearance of these pseudo-phases and the nature of non-stoichiometry is explained in terms of a plausible model invoking microdomain texture in defect solids. This model is believed to be appropriate for other non-stoichiometric systems also. Earlier experimental data on the system are examined, and found to be consistent with the present results.

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