Characteristic behaviors in an ultrathin Ising film with site- (or bond-) dilution at the surfaces

2014 ◽  
Vol 436 ◽  
pp. 208-214 ◽  
Author(s):  
T. Kaneyoshi
Keyword(s):  
Bond Dilution

Critical properties of a random transverse crystal field Ising model with bond dilution

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Ling Wen ◽  
Yan Shi-Lei
Keyword(s):  
Ising Model ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Effective Field ◽  
Square Lattice ◽  
Critical Properties ◽  
Strong Bond ◽  
Ordered Phases ◽  
Bond Dilution ◽  
Global Phase Diagrams

AbstractWithin effective field theory (EFT), the critical properties of a random transverse crystal field Ising model with bond dilution are studied on a square lattice. Under both weak and strong bond dilution conditions, we consider three cases (α = 0,±0.5) of a transverse crystal field ratio, obtaining global phase diagrams in T−D x space for changes in the random transverse crystal field concentration. The phase diagrams obtained for a weak bond dilution are very similar in shape to those of pure bond but with decreases in corresponding ordered phases and critical values. However, the phase diagrams for a strong bond dilution exhibit varieties, including a change in reentrant phenomenon, the occurrence of transverse crystal field degeneration, and the opposite direction crossover of temperature peak value.

Scaling Theory of Elasticity and Fracture in Disordered Networks

1990 ◽  
Vol 207 ◽  
Author(s):  
P. M. Duxbury ◽  
S. G. Kim
Keyword(s):  
Effective Medium Theory ◽  
Theory Of Elasticity ◽  
Central Force ◽  
Scaling Theory ◽  
Tensile Fracture ◽  
Medium Theory ◽  
Bond Dilution ◽  
Disordered Networks ◽  
Dilute Limit ◽  
Force Network

AbstractWe discuss scaling theories for the elasticity and tensile fracture of random central force spring networks with bond dilution disorder. Effective medium theory works quite well for elasticity but needs very new ingredients to be even qualitatively correct for tensile fracture. A novel “extreme scaling theory” predicts a dilute limit singularity and a size effect in the tensile strength. These predictions are supported by numerical simulations.We extend the above arguments to networks with distributions of bond disorder, and compare the central force network theories to models currently used in the study of rigid cellular materials.

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