PHASE STRUCTURE OF THE THREE-DIMENSIONAL $g (\vec {\bf \phi}^2)^2$ FIELD THEORY

1992 ◽  
Vol 07 (05) ◽  
pp. 987-1006 ◽  
Author(s):  
G. V. EFIMOV ◽  
S. N. NEDELKO
Keyword(s):  
Phase Structure ◽  
Field Model ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Symmetric System ◽  
Canonical Transformations ◽  
Coupling Constant ◽  
Large Coupling ◽  
Large Coupling Constant ◽  
Invariant Interaction

The phase structure of the three-dimensional superrenormalizable scalar-field model with the O (N)-invariant interaction g(ϕ2)2 is considered. By the method of canonical transformations, it is shown that this model describes the O (N)-symmetric system at both the small and the large coupling constant g. At the same time, phase transitions accompanied by symmetry rearrangement are possible at intermediate values of g. Comparison with the case of two dimensions shows a crucial influence of higher-order renormalization on the phase structure of the model.

PHASE STRUCTURE OF THREE- AND FOUR-DIMENSIONAL ϕ4 FIELD THEORY

1992 ◽  
Vol 07 (19) ◽  
pp. 4539-4558 ◽  
Author(s):  
G.V. EFIMOV ◽  
S.N. NEDELKO
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Strong Coupling ◽  
Phase Structure ◽  
Space Time ◽  
Strong Coupling Regime ◽  
Canonical Transformations ◽  
Coupling Constant ◽  
Large Coupling ◽  
Large Coupling Constant

The strong coupling regime of gϕ4 theory in space-time Rd for d=3, 4 is investigated by the methods of canonical transformations and the renormalization group. It is shown that the model describes a system symmetric under transformation ϕ→−ϕ both at small and large coupling constant g. Comparison with the case d=2 shows a crucial influence of the renormalization structure of the theory on its phase structure.

scholarly journals Preparation and Spectroscopic Characterization of trans-Fe(CO)3L1L2 (L1, L2 = Phosphine or Phosphite)

1989 ◽  
Vol 44 (6) ◽  
pp. 641-646 ◽  
Author(s):  
Hidenari Inoue ◽  
Takeshi Kuroiwa ◽  
Tsuneo Shirai ◽  
Ekkehard Fluck
Keyword(s):  
Spectroscopic Characterization ◽  
Coupling Constant ◽  
Positive Slope ◽  
Phosphorus Ligands ◽  
Large Coupling ◽  
Iron Carbonyls ◽  
Trigonal Bipyramidal ◽  
Large Coupling Constant ◽  
Back Donation

The 57Fe Mößbauer spectra of mixed ligand complexes of the type trans-Fe(CO)3L1L2 (L1 = triphenylphosphine or triphenylphosphite and L2 = phosphine or phosphite) show a quadrupolesplitting doublet typical of the disubstituted iron carbonyls in trigonal bipyramidal symmetry. The inverse linear dependence of the isomer shifts on the CO stretching frequencies is interpreted on the basis of the strengthening triple-bond nature of the carbonyl ligands with increasing iron-to-phosphorus π-back donation. A linear correlation, with a positive slope, between the isomer shifts and the quadrupole splittings has revealed that the phosphorus-to-iron σ-donation is offset by the iron-to-phosphorus π-back donation. A correlation between the coordination shifts and the isomer shifts demonstrates that the iron-to-phosphorus π-back donation plays an important role in the Fe-P bond. The relatively large coupling constant of 2J(P,P) reflects a strong interaction between trans-phosphorus ligands through the P-Fe-P bond

Simulation of Ideal Grain Growth Using the Multi-Phase-Field Model

2007 ◽  
Vol 558-559 ◽  
pp. 1177-1181 ◽  
Author(s):  
Philippe Schaffnit ◽  
Markus Apel ◽  
Ingo Steinbach
Keyword(s):  
Grain Size ◽  
Grain Growth ◽  
Phase Field ◽  
Large Scale ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Two Dimensions ◽  
Von Neumann ◽  
Average Grain Size

The kinetics and topology of ideal grain growth were simulated using the phase-field model. Large scale phase-field simulations were carried out where ten thousands grains evolved into a few hundreds without allowing coalescence of grains. The implementation was first validated in two-dimensions by checking the conformance with square-root evolution of the average grain size and the von Neumann-Mullins law. Afterwards three-dimensional simulations were performed which also showed fair agreement with the law describing the evolution of the mean grain size against time and with the results of S. Hilgenfeld et al. in 'An Accurate von Neumann's Law for Three-Dimensional Foams', Phys. Rev. Letters, 86(12)/2685, March 2001. Finally the steady state grain size distribution was investigated and compared to the Hillert theory.

scholarly journals Four-pomeron vertex

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
M. A. Braun
Keyword(s):  
Perturbative Qcd ◽  
Variational Approach ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Infrared Region ◽  
The Other ◽  
Coupling Constant ◽  
Large Coupling ◽  
Large Coupling Constant

AbstractThe four-pomeron vertex is studied in the perturbative QCD. Its dominating terms of the leading (zeroth and first) orders in the coupling constant and subdominant in the number of colors are constructed. The vertex consists of two terms, one with a derivative in rapidity $$\partial _y$$ ∂ y and the other with the BFKL interaction between pomerons. The corresponding part of the action and equations of motion are found. The iterative solution of the latter is possible only for rapidities smaller than 2 and quite large coupling constant $$\alpha _s$$ α s , of the order or greater than unity, when the quadruple pomeron interaction is relatively small. Also iteration of the part with $$\partial _y$$ ∂ y is unstable in the infrared region and compels to introduce an infrared cut. The variational approach with simple trying functions allows to find the minimum of the action at $$\alpha _s$$ α s of the order 0.2 and rapidities up to 25. Numerical estimates for O–O collisions show that actually the influence of the quadruple pomeron interaction turns out to be rather small.

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