Statistical Mechanics of a Compressible Ising Model with Application to β Brass

1971 ◽  
Vol 55 (2) ◽  
pp. 861-879 ◽  
Author(s):  
George A. Baker ◽  
John W. Essam
Keyword(s):  
Ising Model ◽  
Statistical Mechanics

scholarly journals Order-disorder statistics. I

1949 ◽  
Vol 196 (1044) ◽  
pp. 36-50 ◽  
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Infinite Matrix ◽  
Characteristic Structure ◽  
Single Function ◽  
Simple Characteristic ◽  
Distant Neighbour ◽  
Function Of Two Variables

In 1941 Kramers & Wannier discussed the statistical mechanics of a two-dimensional Ising model of a ferromagnetic. By making use of a ‘screw transformation’ they showed that the partition function was the largest eigenvalue of an infinite matrix of simple characteristic structure. In the present paper an alternative method is used for deriving the partition function, and this enables the ‘screw transformation’ to be generalized to apply to a number of problems of classical statistical mechanics, including the three-dimensional Ising model. Distant neighbour interactions can also be taken into account. The relation between the ferromagnetic and order-disorder problems is discussed, and it is shown that the partition function in both cases can be derived from a single function of two variables. Since distant neighbour interactions can be taken into account the theory can be formally applied to the statistical mechanics of a system of identical particles.

scholarly journals Statistical mechanics of the cluster Ising model

2011 ◽  
Vol 84 (2) ◽  
Author(s):  
Pietro Smacchia ◽  
Luigi Amico ◽  
Paolo Facchi ◽  
Rosario Fazio ◽  
Giuseppe Florio ◽  
...  
Keyword(s):  
Ising Model ◽  
Statistical Mechanics

Statistical mechanics of the two-dimensional assembly

1950 ◽  
Vol 202 (1069) ◽  
pp. 202-207 ◽  
Keyword(s):  
Ising Model ◽  
Curie Temperature ◽  
Statistical Mechanics ◽  
Specific Heat ◽  
Considerable Effect ◽  
Square Lattice ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Triangular Lattices

The work of Kaufman & Onsager (1946) on the two-dimensional Ising model of a ferromagnet is extended from the plane square lattice to the plane honeycomb and triangular lattices. The specific heat anomaly, where it exists, turns out to be of the same type in all three lattices, an infinity in the specific heat at the Curie temperature. It is concluded that second-nearest neighbour interactions may have a considerable effect on the position of the Curie temperature.

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