scholarly journals On the statistical mechanics of the gauge invariant Ising model

1979 ◽  
Vol 67 (3) ◽  
pp. 233-240 ◽  
Author(s):  
R. Marra ◽  
S. Miracle-Sole
Keyword(s):  
Ising Model ◽  
Statistical Mechanics ◽  
Gauge Invariant

Gauge fields on a lattice. II. Gauge-invariant Ising model

1975 ◽  
Vol 11 (8) ◽  
pp. 2098-2103 ◽  
Author(s):  
R. Balian ◽  
J. M. Drouffe ◽  
C. Itzykson
Keyword(s):  
Ising Model ◽  
Gauge Fields ◽  
Gauge Invariant

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.

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