Onset of long-range order in superlattices: Mean-field theory

1992 ◽  
Vol 46 (18) ◽  
pp. 11681-11687 ◽  
Author(s):  
R. W. Wang ◽  
D. L. Mills
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Range Order ◽  
Long Range Order

Long-Range Order and Short-Range Order inPd3V: Breakdown of the Mean-Field Theory

1987 ◽  
Vol 58 (21) ◽  
pp. 2245-2248 ◽  
Author(s):  
F. Solal ◽  
R. Caudron ◽  
F. Ducastelle ◽  
A. Finel ◽  
A. Loiseau
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Short Range ◽  
Short Range Order ◽  
Mean Field Theory ◽  
Mean Field ◽  
Range Order ◽  
Long Range Order ◽  
The Mean

scholarly journals Bonding Energies and Long-Range Order in the Trialuminides

1990 ◽  
Vol 213 ◽  
Author(s):  
C. J. Sparks ◽  
E. D. Specht ◽  
G. E. Ice ◽  
P. Zschack ◽  
J. Schneibel
Keyword(s):  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Energy Difference ◽  
Near Neighbor ◽  
Range Order ◽  
Theory Approach ◽  
Long Range Order ◽  
Bond Energies ◽  
Pair Potentials

ABSTRACTThe degree of long-range order in the trialuminides is determined by X-ray powder diffraction techniques. Long-range order exists to their melting points. For the binary trialuminides Al3Ti, Al73Ti27, and Al3Sc, the degree of long-range order is nearly perfect and is a measure of the lack of mixing of the aluminum atoms onto the sublattice occupied by either Ti or Sc. A calculation of the bond energy between neighboring pairs of atoms from the ordering (melting) temperature is made following the Bragg-Williams mean field theory approach. These bond energies compare favorably with more sophisticated calculations. Bond energies are found to be larger than the energy difference between the crystal structure forms DO22, Ll2, and DO23, and therefore, more relevant to understanding the mechanical and chemical behavior of the trialuminides. Ordering or melting temperatures of these intermetallics reflect the strong Al-metal near-neighbor pair potentials and may provide insights to their brittle properties.

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

ABSENCE OF PHASE TRANSITIONS ON TREE STRUCTURES

1993 ◽  
Vol 07 (29n30) ◽  
pp. 1947-1950 ◽  
Author(s):  
RAFFAELLA BURIONI ◽  
DAVIDE CASSI
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Linear Chain ◽  
Mean Field ◽  
Range Order ◽  
The Other ◽  
Long Range Order ◽  
Field Phase ◽  
Tree Structures ◽  
Bethe Lattices

We rigorously prove that the correlation functions of any statistical model having a compact transitive symmetry group and nearest-neighbor interactions on any tree structure are equal to the corresponding ones on a linear chain. The exponential decay of the latter implies the absence of long-range order on any tree. On the other hand, for trees with exponential growth such as Bethe lattices, one can show the existence of a particular kind of mean field phase transition without long-range order.

Mean-field theory for the long-range contact process with diffusion

2015 ◽  
Vol 92 (3) ◽  
Author(s):  
T. B. Pedro ◽  
W. Figueiredo ◽  
A. L. Ferreira
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Contact Process ◽  
Mean Field Theory ◽  
Mean Field
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