Algebraic Derivation of the Partition Function of a Two‐Dimensional Ising Model

1965 ◽  
Vol 6 (9) ◽  
pp. 1392-1395 ◽  
Author(s):  
Colin J. Thompson
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Two Dimensional

The cooperative behaviour of a two-dimensional defect crystal

1957 ◽  
Vol 53 (4) ◽  
pp. 863-869 ◽  
Author(s):  
E. W. Elcock
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Logarithmic Singularity ◽  
Perfect Crystal ◽  
Cooperative Behaviour ◽  
Two Dimensional ◽  
Combinatorial Method ◽  
Ferromagnetic Crystal ◽  
Defect Crystal ◽  
Lower Temperature

ABSTRACTThe Ising model of a two-dimensional ferromagnetic crystal containing defects is considered. It is shown that the combinatorial method is particularly appropriate to the investigation of the two-dimensional defect crystal and how it may be readily modified to calculate the partition function for such a crystal. It is found that the cooperative behaviour of the infinite perfect crystal, as indicated by the occurrence of a logarithmic singularity in the specific heat as a function of temperature, is not destroyed in the defect crystal; the singularity persists, though at a progressively lower temperature as the density of defects is increased, until a high density of defects is reached. The value of this limiting density of defects, above which the cooperative behaviour is destroyed, is calculated.

scholarly journals Two-dimensional Ising Model on a 4?6?12 Lattice

1985 ◽  
Vol 38 (2) ◽  
pp. 227
Author(s):  
KY Lin ◽  
WN Huang
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Two Dimensional ◽  
Special Case

We have considered a two-dimensional Ising model on a 4-6-12 lattice. The partition function is evaluated exactly by the method of Pfaffian. The Ising model on a ruby lattice is a special case of our model.

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